---
_id: '63213'
abstract:
- lang: eng
  text: '<jats:p>Quantum uncertainty relations impose fundamental limits on the joint
    knowledge that can be acquired from complementary observables: Perfect knowledge
    of a quantum state in one basis implies maximal indetermination in all other mutually
    unbiased bases (MUBs). Uncertainty relations derived from joint properties of
    the MUBs are generally assumed to be uniform, irrespective of the specific observables
    chosen within a set. In this work, we demonstrate instead that the uncertainty
    relations can depend on the choice of observables. Through both experimental observation
    and numerical methods, we show that selecting different sets of three MUBs in
    a five-dimensional quantum system results in distinct uncertainty bounds, i.e.,
    in varying degrees of complementarity, in terms of both entropy and variance.</jats:p>'
article_number: '033152'
article_type: original
author:
- first_name: Laura Maria
  full_name: Serino, Laura Maria
  id: '88242'
  last_name: Serino
- first_name: Giovanni
  full_name: Chesi, Giovanni
  last_name: Chesi
- first_name: Benjamin
  full_name: Brecht, Benjamin
  id: '27150'
  last_name: Brecht
  orcid: '0000-0003-4140-0556 '
- first_name: Lorenzo
  full_name: Maccone, Lorenzo
  last_name: Maccone
- first_name: Chiara
  full_name: Macchiavello, Chiara
  last_name: Macchiavello
- first_name: Christine
  full_name: Silberhorn, Christine
  id: '26263'
  last_name: Silberhorn
citation:
  ama: 'Serino LM, Chesi G, Brecht B, Maccone L, Macchiavello C, Silberhorn C. Complementarity-based
    complementarity: The choice of mutually unbiased observables shapes quantum uncertainty
    relations. <i>Physical Review Research</i>. 2025;7(3). doi:<a href="https://doi.org/10.1103/v24q-sl6n">10.1103/v24q-sl6n</a>'
  apa: 'Serino, L. M., Chesi, G., Brecht, B., Maccone, L., Macchiavello, C., &#38;
    Silberhorn, C. (2025). Complementarity-based complementarity: The choice of mutually
    unbiased observables shapes quantum uncertainty relations. <i>Physical Review
    Research</i>, <i>7</i>(3), Article 033152. <a href="https://doi.org/10.1103/v24q-sl6n">https://doi.org/10.1103/v24q-sl6n</a>'
  bibtex: '@article{Serino_Chesi_Brecht_Maccone_Macchiavello_Silberhorn_2025, title={Complementarity-based
    complementarity: The choice of mutually unbiased observables shapes quantum uncertainty
    relations}, volume={7}, DOI={<a href="https://doi.org/10.1103/v24q-sl6n">10.1103/v24q-sl6n</a>},
    number={3033152}, journal={Physical Review Research}, publisher={American Physical
    Society (APS)}, author={Serino, Laura Maria and Chesi, Giovanni and Brecht, Benjamin
    and Maccone, Lorenzo and Macchiavello, Chiara and Silberhorn, Christine}, year={2025}
    }'
  chicago: 'Serino, Laura Maria, Giovanni Chesi, Benjamin Brecht, Lorenzo Maccone,
    Chiara Macchiavello, and Christine Silberhorn. “Complementarity-Based Complementarity:
    The Choice of Mutually Unbiased Observables Shapes Quantum Uncertainty Relations.”
    <i>Physical Review Research</i> 7, no. 3 (2025). <a href="https://doi.org/10.1103/v24q-sl6n">https://doi.org/10.1103/v24q-sl6n</a>.'
  ieee: 'L. M. Serino, G. Chesi, B. Brecht, L. Maccone, C. Macchiavello, and C. Silberhorn,
    “Complementarity-based complementarity: The choice of mutually unbiased observables
    shapes quantum uncertainty relations,” <i>Physical Review Research</i>, vol. 7,
    no. 3, Art. no. 033152, 2025, doi: <a href="https://doi.org/10.1103/v24q-sl6n">10.1103/v24q-sl6n</a>.'
  mla: 'Serino, Laura Maria, et al. “Complementarity-Based Complementarity: The Choice
    of Mutually Unbiased Observables Shapes Quantum Uncertainty Relations.” <i>Physical
    Review Research</i>, vol. 7, no. 3, 033152, American Physical Society (APS), 2025,
    doi:<a href="https://doi.org/10.1103/v24q-sl6n">10.1103/v24q-sl6n</a>.'
  short: L.M. Serino, G. Chesi, B. Brecht, L. Maccone, C. Macchiavello, C. Silberhorn,
    Physical Review Research 7 (2025).
date_created: 2025-12-18T16:04:45Z
date_updated: 2025-12-18T16:05:45Z
department:
- _id: '15'
- _id: '623'
doi: 10.1103/v24q-sl6n
intvolume: '         7'
issue: '3'
language:
- iso: eng
publication: Physical Review Research
publication_identifier:
  issn:
  - 2643-1564
publication_status: published
publisher: American Physical Society (APS)
status: public
title: 'Complementarity-based complementarity: The choice of mutually unbiased observables
  shapes quantum uncertainty relations'
type: journal_article
user_id: '27150'
volume: 7
year: '2025'
...
---
_id: '63212'
author:
- first_name: Josef
  full_name: Riese, Josef
  id: '429'
  last_name: Riese
  orcid: 0000-0003-2927-2619
- first_name: Peter
  full_name: Reinhold, Peter
  id: '416'
  last_name: Reinhold
citation:
  ama: 'Riese J, Reinhold P. Physik in der Lehrerinnen- und Lehrerbildung - Empirisch
    fundierte Curricula in einer digitalen Welt. In: Cramer C, König J, Rothland M,
    eds. <i>Handbuch Lehrerinnen- und Lehrerbildung</i>. 2nd ed. Verlag Julius Klinkhardt;
    2025. doi:<a href="https://doi.org/10.35468/hblb2025-076">10.35468/hblb2025-076</a>'
  apa: Riese, J., &#38; Reinhold, P. (2025). Physik in der Lehrerinnen- und Lehrerbildung
    - Empirisch fundierte Curricula in einer digitalen Welt. In C. Cramer, J. König,
    &#38; M. Rothland (Eds.), <i>Handbuch Lehrerinnen- und Lehrerbildung</i> (2nd
    ed.). Verlag Julius Klinkhardt. <a href="https://doi.org/10.35468/hblb2025-076">https://doi.org/10.35468/hblb2025-076</a>
  bibtex: '@inbook{Riese_Reinhold_2025, place={Bad Heilbrunn}, edition={2}, title={Physik
    in der Lehrerinnen- und Lehrerbildung - Empirisch fundierte Curricula in einer
    digitalen Welt}, DOI={<a href="https://doi.org/10.35468/hblb2025-076">10.35468/hblb2025-076</a>},
    booktitle={Handbuch Lehrerinnen- und Lehrerbildung}, publisher={Verlag Julius
    Klinkhardt}, author={Riese, Josef and Reinhold, Peter}, editor={Cramer, Colin
    and König, Johannes  and Rothland, Martin}, year={2025} }'
  chicago: 'Riese, Josef, and Peter Reinhold. “Physik in der Lehrerinnen- und Lehrerbildung
    - Empirisch fundierte Curricula in einer digitalen Welt.” In <i>Handbuch Lehrerinnen-
    und Lehrerbildung</i>, edited by Colin Cramer, Johannes  König, and Martin Rothland,
    2nd ed. Bad Heilbrunn: Verlag Julius Klinkhardt, 2025. <a href="https://doi.org/10.35468/hblb2025-076">https://doi.org/10.35468/hblb2025-076</a>.'
  ieee: 'J. Riese and P. Reinhold, “Physik in der Lehrerinnen- und Lehrerbildung -
    Empirisch fundierte Curricula in einer digitalen Welt,” in <i>Handbuch Lehrerinnen-
    und Lehrerbildung</i>, 2nd ed., C. Cramer, J. König, and M. Rothland, Eds. Bad
    Heilbrunn: Verlag Julius Klinkhardt, 2025.'
  mla: Riese, Josef, and Peter Reinhold. “Physik in der Lehrerinnen- und Lehrerbildung
    - Empirisch fundierte Curricula in einer digitalen Welt.” <i>Handbuch Lehrerinnen-
    und Lehrerbildung</i>, edited by Colin Cramer et al., 2nd ed., Verlag Julius Klinkhardt,
    2025, doi:<a href="https://doi.org/10.35468/hblb2025-076">10.35468/hblb2025-076</a>.
  short: 'J. Riese, P. Reinhold, in: C. Cramer, J. König, M. Rothland (Eds.), Handbuch
    Lehrerinnen- und Lehrerbildung, 2nd ed., Verlag Julius Klinkhardt, Bad Heilbrunn,
    2025.'
date_created: 2025-12-18T14:53:55Z
date_updated: 2025-12-18T15:04:58Z
department:
- _id: '299'
doi: 10.35468/hblb2025-076
edition: '2'
editor:
- first_name: Colin
  full_name: Cramer, Colin
  last_name: Cramer
- first_name: 'Johannes '
  full_name: 'König, Johannes '
  last_name: König
- first_name: Martin
  full_name: Rothland, Martin
  last_name: Rothland
language:
- iso: ger
place: Bad Heilbrunn
publication: Handbuch Lehrerinnen- und Lehrerbildung
publication_identifier:
  isbn:
  - 978-3-8365-6544-6
publication_status: published
publisher: Verlag Julius Klinkhardt
status: public
title: Physik in der Lehrerinnen- und Lehrerbildung - Empirisch fundierte Curricula
  in einer digitalen Welt
type: book_chapter
user_id: '429'
year: '2025'
...
---
_id: '63187'
author:
- first_name: Arnott Jeffery Joel
  full_name: Kidner, Arnott Jeffery Joel
  id: '111755'
  last_name: Kidner
- first_name: Eckhard
  full_name: Steffen, Eckhard
  id: '15548'
  last_name: Steffen
  orcid: 0000-0002-9808-7401
- first_name: Weiqiang
  full_name: Yu, Weiqiang
  id: '117508'
  last_name: Yu
citation:
  ama: Kidner AJJ, Steffen E, Yu W. Edge-coloring 4- and 5-regular projective planar
    graphs with no Petersen-minor. <i>arXiv:251214285</i>. Published online 2025.
  apa: Kidner, A. J. J., Steffen, E., &#38; Yu, W. (2025). Edge-coloring 4- and 5-regular
    projective planar graphs with no Petersen-minor. In <i>arXiv:2512.14285</i>.
  bibtex: '@article{Kidner_Steffen_Yu_2025, title={Edge-coloring 4- and 5-regular
    projective planar graphs with no Petersen-minor}, journal={arXiv:2512.14285},
    author={Kidner, Arnott Jeffery Joel and Steffen, Eckhard and Yu, Weiqiang}, year={2025}
    }'
  chicago: Kidner, Arnott Jeffery Joel, Eckhard Steffen, and Weiqiang Yu. “Edge-Coloring
    4- and 5-Regular Projective Planar Graphs with No Petersen-Minor.” <i>ArXiv:2512.14285</i>,
    2025.
  ieee: A. J. J. Kidner, E. Steffen, and W. Yu, “Edge-coloring 4- and 5-regular projective
    planar graphs with no Petersen-minor,” <i>arXiv:2512.14285</i>. 2025.
  mla: Kidner, Arnott Jeffery Joel, et al. “Edge-Coloring 4- and 5-Regular Projective
    Planar Graphs with No Petersen-Minor.” <i>ArXiv:2512.14285</i>, 2025.
  short: A.J.J. Kidner, E. Steffen, W. Yu, ArXiv:2512.14285 (2025).
date_created: 2025-12-17T14:40:23Z
date_updated: 2025-12-18T13:17:18Z
department:
- _id: '542'
external_id:
  arxiv:
  - '2512.14285'
language:
- iso: eng
publication: arXiv:2512.14285
status: public
title: Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor
type: preprint
user_id: '15540'
year: '2025'
...
---
_id: '63214'
abstract:
- lang: eng
  text: <jats:p>We study a possibility of measuring the time-resolved second-order
    autocorrelation function of one of two beams generated in type-II parametric down-conversion
    by means of temporal magnification of this beam, bringing its correlation time
    from the picosecond to the nanosecond scale, which can be resolved by modern photodetectors.
    We show that such a measurement enables one to infer directly the degree of global
    coherence of that beam, which is linked by a simple relation to the number of
    modes characterizing the entanglement between the two generated beams. We illustrate
    the proposed method by an example of photon pairs generated in a periodically
    poled potassium titanyl phosphate (KTP) crystal with a symmetric group velocity
    matching for various durations of the pump pulse, resulting in different numbers
    of modes. Our theoretical model also shows that the magnified double-heralded
    autocorrelation function of one beam exhibits a local maximum around zero delay
    time, corresponding to photon bunching at a short time scale.</jats:p>
article_number: '023703'
author:
- first_name: Dmitri B.
  full_name: Horoshko, Dmitri B.
  last_name: Horoshko
- first_name: Shivang
  full_name: Srivastava, Shivang
  last_name: Srivastava
- first_name: Filip
  full_name: Sośnicki, Filip
  last_name: Sośnicki
- first_name: Michał
  full_name: Mikołajczyk, Michał
  last_name: Mikołajczyk
- first_name: Michał
  full_name: Karpiński, Michał
  last_name: Karpiński
- first_name: Benjamin
  full_name: Brecht, Benjamin
  id: '27150'
  last_name: Brecht
  orcid: '0000-0003-4140-0556 '
- first_name: Mikhail I.
  full_name: Kolobov, Mikhail I.
  last_name: Kolobov
citation:
  ama: Horoshko DB, Srivastava S, Sośnicki F, et al. Time-resolved second-order autocorrelation
    function of parametric down-conversion. <i>Physical Review A</i>. 2025;112(2).
    doi:<a href="https://doi.org/10.1103/7ckm-tm3r">10.1103/7ckm-tm3r</a>
  apa: Horoshko, D. B., Srivastava, S., Sośnicki, F., Mikołajczyk, M., Karpiński,
    M., Brecht, B., &#38; Kolobov, M. I. (2025). Time-resolved second-order autocorrelation
    function of parametric down-conversion. <i>Physical Review A</i>, <i>112</i>(2),
    Article 023703. <a href="https://doi.org/10.1103/7ckm-tm3r">https://doi.org/10.1103/7ckm-tm3r</a>
  bibtex: '@article{Horoshko_Srivastava_Sośnicki_Mikołajczyk_Karpiński_Brecht_Kolobov_2025,
    title={Time-resolved second-order autocorrelation function of parametric down-conversion},
    volume={112}, DOI={<a href="https://doi.org/10.1103/7ckm-tm3r">10.1103/7ckm-tm3r</a>},
    number={2023703}, journal={Physical Review A}, publisher={American Physical Society
    (APS)}, author={Horoshko, Dmitri B. and Srivastava, Shivang and Sośnicki, Filip
    and Mikołajczyk, Michał and Karpiński, Michał and Brecht, Benjamin and Kolobov,
    Mikhail I.}, year={2025} }'
  chicago: Horoshko, Dmitri B., Shivang Srivastava, Filip Sośnicki, Michał Mikołajczyk,
    Michał Karpiński, Benjamin Brecht, and Mikhail I. Kolobov. “Time-Resolved Second-Order
    Autocorrelation Function of Parametric down-Conversion.” <i>Physical Review A</i>
    112, no. 2 (2025). <a href="https://doi.org/10.1103/7ckm-tm3r">https://doi.org/10.1103/7ckm-tm3r</a>.
  ieee: 'D. B. Horoshko <i>et al.</i>, “Time-resolved second-order autocorrelation
    function of parametric down-conversion,” <i>Physical Review A</i>, vol. 112, no.
    2, Art. no. 023703, 2025, doi: <a href="https://doi.org/10.1103/7ckm-tm3r">10.1103/7ckm-tm3r</a>.'
  mla: Horoshko, Dmitri B., et al. “Time-Resolved Second-Order Autocorrelation Function
    of Parametric down-Conversion.” <i>Physical Review A</i>, vol. 112, no. 2, 023703,
    American Physical Society (APS), 2025, doi:<a href="https://doi.org/10.1103/7ckm-tm3r">10.1103/7ckm-tm3r</a>.
  short: D.B. Horoshko, S. Srivastava, F. Sośnicki, M. Mikołajczyk, M. Karpiński,
    B. Brecht, M.I. Kolobov, Physical Review A 112 (2025).
date_created: 2025-12-18T16:06:13Z
date_updated: 2025-12-18T16:06:34Z
department:
- _id: '15'
- _id: '623'
doi: 10.1103/7ckm-tm3r
intvolume: '       112'
issue: '2'
language:
- iso: eng
publication: Physical Review A
publication_identifier:
  issn:
  - 2469-9926
  - 2469-9934
publication_status: published
publisher: American Physical Society (APS)
status: public
title: Time-resolved second-order autocorrelation function of parametric down-conversion
type: journal_article
user_id: '27150'
volume: 112
year: '2025'
...
---
_id: '63215'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n               <jats:p>High-dimensional
    time-frequency encodings have the potential to significantly advance quantum information
    science; however, practical applications require precise knowledge of the encoded
    quantum states, which becomes increasingly challenging for larger Hilbert spaces.
    Self-guided tomography (SGT) has emerged as a practical and scalable technique
    for this purpose in the spatial domain. Here, we apply SGT to estimate time-frequency
    states using a multi-output quantum pulse gate. We achieve fidelities of more
    than 99% for 3- and 5-dimensional states without the need for calibration or post-processing.
    We demonstrate the robustness of SGT against statistical and environmental noise,
    highlighting its efficacy in the photon-starved regime typical of quantum information
    applications.</jats:p>"
article_number: '025024'
author:
- first_name: Laura Maria
  full_name: Serino, Laura Maria
  id: '88242'
  last_name: Serino
- first_name: Markus
  full_name: Rambach, Markus
  last_name: Rambach
- first_name: Benjamin
  full_name: Brecht, Benjamin
  id: '27150'
  last_name: Brecht
  orcid: '0000-0003-4140-0556 '
- first_name: Jacquiline
  full_name: Romero, Jacquiline
  last_name: Romero
- first_name: Christine
  full_name: Silberhorn, Christine
  id: '26263'
  last_name: Silberhorn
citation:
  ama: Serino LM, Rambach M, Brecht B, Romero J, Silberhorn C. Self-guided tomography
    of time-frequency qudits. <i>Quantum Science and Technology</i>. 2025;10(2). doi:<a
    href="https://doi.org/10.1088/2058-9565/adb0ea">10.1088/2058-9565/adb0ea</a>
  apa: Serino, L. M., Rambach, M., Brecht, B., Romero, J., &#38; Silberhorn, C. (2025).
    Self-guided tomography of time-frequency qudits. <i>Quantum Science and Technology</i>,
    <i>10</i>(2), Article 025024. <a href="https://doi.org/10.1088/2058-9565/adb0ea">https://doi.org/10.1088/2058-9565/adb0ea</a>
  bibtex: '@article{Serino_Rambach_Brecht_Romero_Silberhorn_2025, title={Self-guided
    tomography of time-frequency qudits}, volume={10}, DOI={<a href="https://doi.org/10.1088/2058-9565/adb0ea">10.1088/2058-9565/adb0ea</a>},
    number={2025024}, journal={Quantum Science and Technology}, publisher={IOP Publishing},
    author={Serino, Laura Maria and Rambach, Markus and Brecht, Benjamin and Romero,
    Jacquiline and Silberhorn, Christine}, year={2025} }'
  chicago: Serino, Laura Maria, Markus Rambach, Benjamin Brecht, Jacquiline Romero,
    and Christine Silberhorn. “Self-Guided Tomography of Time-Frequency Qudits.” <i>Quantum
    Science and Technology</i> 10, no. 2 (2025). <a href="https://doi.org/10.1088/2058-9565/adb0ea">https://doi.org/10.1088/2058-9565/adb0ea</a>.
  ieee: 'L. M. Serino, M. Rambach, B. Brecht, J. Romero, and C. Silberhorn, “Self-guided
    tomography of time-frequency qudits,” <i>Quantum Science and Technology</i>, vol.
    10, no. 2, Art. no. 025024, 2025, doi: <a href="https://doi.org/10.1088/2058-9565/adb0ea">10.1088/2058-9565/adb0ea</a>.'
  mla: Serino, Laura Maria, et al. “Self-Guided Tomography of Time-Frequency Qudits.”
    <i>Quantum Science and Technology</i>, vol. 10, no. 2, 025024, IOP Publishing,
    2025, doi:<a href="https://doi.org/10.1088/2058-9565/adb0ea">10.1088/2058-9565/adb0ea</a>.
  short: L.M. Serino, M. Rambach, B. Brecht, J. Romero, C. Silberhorn, Quantum Science
    and Technology 10 (2025).
date_created: 2025-12-18T16:07:11Z
date_updated: 2025-12-18T16:07:35Z
department:
- _id: '15'
- _id: '623'
doi: 10.1088/2058-9565/adb0ea
intvolume: '        10'
issue: '2'
language:
- iso: eng
publication: Quantum Science and Technology
publication_identifier:
  issn:
  - 2058-9565
publication_status: published
publisher: IOP Publishing
status: public
title: Self-guided tomography of time-frequency qudits
type: journal_article
user_id: '27150'
volume: 10
year: '2025'
...
---
_id: '63223'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>The quartz crystal microbalance with
    dissipation monitoring (QCM‐D) is routinely used to investigate structured samples.
    Here, a simulation technique is described, that predicts the shifts of frequency
    and half bandwidth, Δ<jats:italic>f<jats:sub>n</jats:sub></jats:italic> and ΔΓ<jats:italic><jats:sub>n</jats:sub></jats:italic>,
    of a quartz resonator operating on different overtone orders, <jats:italic>n</jats:italic>,
    induced by structured samples in contact with the resonator surface in liquid.
    The technique, abbreviated as FreqD‐LBM, solves the Stokes equation in the frequency
    domain. The solution provides the complex amplitude of the area‐averaged tangential
    stress at the resonator surface, from which Δ<jats:italic>f<jats:sub>n</jats:sub></jats:italic>
    and ΔΓ<jats:italic><jats:sub>n</jats:sub></jats:italic> are derived. Because the
    dynamical variables are complex amplitudes, the viscosity can be complex, as well.
    The technique naturally covers viscoelasticity. Limitations are linked to the
    grid resolution and to problems at large viscosity. Validation steps include viscoelastic
    films, rough surfaces, an oscillating cylinder in a viscous medium, and a free‐floating
    sphere above the resonator. Application examples are soft adsorbed particles,
    stiff adsorbed particles, and a large, immobile spherical cap above the resonator,
    which allows to study the high‐frequency properties of the material in the gap.
    FreqDLBM runs on an office PC and does not require expert knowledge of numerical
    techniques. It is accessible to an experimentalist.</jats:p>
article_number: '2401373'
article_type: original
author:
- first_name: Diethelm
  full_name: Johannsmann, Diethelm
  last_name: Johannsmann
- first_name: Paul
  full_name: Häusner, Paul
  last_name: Häusner
- first_name: Arne
  full_name: Langhoff, Arne
  last_name: Langhoff
- first_name: Christian
  full_name: Leppin, Christian
  id: '117722'
  last_name: Leppin
- first_name: Ilya
  full_name: Reviakine, Ilya
  last_name: Reviakine
- first_name: Viktor
  full_name: Vanoppen, Viktor
  last_name: Vanoppen
citation:
  ama: 'Johannsmann D, Häusner P, Langhoff A, Leppin C, Reviakine I, Vanoppen V. The
    Frequency‐Domain Lattice Boltzmann Method (FreqD‐LBM): A Versatile Tool to Predict
    the QCM Response Induced by Structured Samples. <i>Advanced Theory and Simulations</i>.
    2025;8(7). doi:<a href="https://doi.org/10.1002/adts.202401373">10.1002/adts.202401373</a>'
  apa: 'Johannsmann, D., Häusner, P., Langhoff, A., Leppin, C., Reviakine, I., &#38;
    Vanoppen, V. (2025). The Frequency‐Domain Lattice Boltzmann Method (FreqD‐LBM):
    A Versatile Tool to Predict the QCM Response Induced by Structured Samples. <i>Advanced
    Theory and Simulations</i>, <i>8</i>(7), Article 2401373. <a href="https://doi.org/10.1002/adts.202401373">https://doi.org/10.1002/adts.202401373</a>'
  bibtex: '@article{Johannsmann_Häusner_Langhoff_Leppin_Reviakine_Vanoppen_2025, title={The
    Frequency‐Domain Lattice Boltzmann Method (FreqD‐LBM): A Versatile Tool to Predict
    the QCM Response Induced by Structured Samples}, volume={8}, DOI={<a href="https://doi.org/10.1002/adts.202401373">10.1002/adts.202401373</a>},
    number={72401373}, journal={Advanced Theory and Simulations}, publisher={Wiley},
    author={Johannsmann, Diethelm and Häusner, Paul and Langhoff, Arne and Leppin,
    Christian and Reviakine, Ilya and Vanoppen, Viktor}, year={2025} }'
  chicago: 'Johannsmann, Diethelm, Paul Häusner, Arne Langhoff, Christian Leppin,
    Ilya Reviakine, and Viktor Vanoppen. “The Frequency‐Domain Lattice Boltzmann Method
    (FreqD‐LBM): A Versatile Tool to Predict the QCM Response Induced by Structured
    Samples.” <i>Advanced Theory and Simulations</i> 8, no. 7 (2025). <a href="https://doi.org/10.1002/adts.202401373">https://doi.org/10.1002/adts.202401373</a>.'
  ieee: 'D. Johannsmann, P. Häusner, A. Langhoff, C. Leppin, I. Reviakine, and V.
    Vanoppen, “The Frequency‐Domain Lattice Boltzmann Method (FreqD‐LBM): A Versatile
    Tool to Predict the QCM Response Induced by Structured Samples,” <i>Advanced Theory
    and Simulations</i>, vol. 8, no. 7, Art. no. 2401373, 2025, doi: <a href="https://doi.org/10.1002/adts.202401373">10.1002/adts.202401373</a>.'
  mla: 'Johannsmann, Diethelm, et al. “The Frequency‐Domain Lattice Boltzmann Method
    (FreqD‐LBM): A Versatile Tool to Predict the QCM Response Induced by Structured
    Samples.” <i>Advanced Theory and Simulations</i>, vol. 8, no. 7, 2401373, Wiley,
    2025, doi:<a href="https://doi.org/10.1002/adts.202401373">10.1002/adts.202401373</a>.'
  short: D. Johannsmann, P. Häusner, A. Langhoff, C. Leppin, I. Reviakine, V. Vanoppen,
    Advanced Theory and Simulations 8 (2025).
date_created: 2025-12-18T16:57:22Z
date_updated: 2025-12-18T17:46:34Z
doi: 10.1002/adts.202401373
intvolume: '         8'
issue: '7'
language:
- iso: eng
publication: Advanced Theory and Simulations
publication_identifier:
  issn:
  - 2513-0390
  - 2513-0390
publication_status: published
publisher: Wiley
quality_controlled: '1'
status: public
title: 'The Frequency‐Domain Lattice Boltzmann Method (FreqD‐LBM): A Versatile Tool
  to Predict the QCM Response Induced by Structured Samples'
type: journal_article
user_id: '117722'
volume: 8
year: '2025'
...
---
_id: '63222'
abstract:
- lang: eng
  text: <jats:p>The solid electrolyte interphase (SEI) on the anode of lithium-ion
    batteries (LIBs) has been studied thoroughly due to its crucial importance to
    the battery’s long-term performance. At the same time, most studies of the SEI
    apply ex situ characterization methods, which may introduce artifacts or misinterpretations
    as they do not investigate the SEI in its unaltered state immersed in liquid battery
    electrolyte. Thus, in this work, we focus on using the non-destructive combination
    of electrochemical quartz crystal microbalance with dissipation monitoring (EQCM-D)
    and impedance spectroscopy (EIS) in the same electrochemical cell. EQCM-D can
    not only probe the solidified products of the SEI but also allows for the monitoring
    of viscoelastic layers and viscosity changes of the electrolyte at the interphase
    during the SEI formation. EIS complements those results by providing electrochemical
    properties of the formed interphase. Our results highlight substantial differences
    in the physical and electrochemical properties between the SEI formed on copper
    and on amorphous carbon and show how formation parameters and the additive vinylene
    carbonate (VC) influence their growth. The EQCM-D results show consistently that
    much thicker SEIs are formed on carbon substrates in comparison to copper substrates.</jats:p>
article_number: '273'
article_type: original
author:
- first_name: Michael
  full_name: Stich, Michael
  last_name: Stich
- first_name: Christian
  full_name: Leppin, Christian
  id: '117722'
  last_name: Leppin
- first_name: Falk Thorsten
  full_name: Krauss, Falk Thorsten
  last_name: Krauss
- first_name: Jesus Eduardo
  full_name: Valdes Landa, Jesus Eduardo
  last_name: Valdes Landa
- first_name: Isabel
  full_name: Pantenburg, Isabel
  last_name: Pantenburg
- first_name: Bernhard
  full_name: Roling, Bernhard
  last_name: Roling
- first_name: Andreas
  full_name: Bund, Andreas
  last_name: Bund
citation:
  ama: 'Stich M, Leppin C, Krauss FT, et al. Comparing the SEI Formation on Copper
    and Amorphous Carbon: A Study with Combined Operando Methods. <i>Batteries</i>.
    2025;11(7). doi:<a href="https://doi.org/10.3390/batteries11070273">10.3390/batteries11070273</a>'
  apa: 'Stich, M., Leppin, C., Krauss, F. T., Valdes Landa, J. E., Pantenburg, I.,
    Roling, B., &#38; Bund, A. (2025). Comparing the SEI Formation on Copper and Amorphous
    Carbon: A Study with Combined Operando Methods. <i>Batteries</i>, <i>11</i>(7),
    Article 273. <a href="https://doi.org/10.3390/batteries11070273">https://doi.org/10.3390/batteries11070273</a>'
  bibtex: '@article{Stich_Leppin_Krauss_Valdes Landa_Pantenburg_Roling_Bund_2025,
    title={Comparing the SEI Formation on Copper and Amorphous Carbon: A Study with
    Combined Operando Methods}, volume={11}, DOI={<a href="https://doi.org/10.3390/batteries11070273">10.3390/batteries11070273</a>},
    number={7273}, journal={Batteries}, publisher={MDPI AG}, author={Stich, Michael
    and Leppin, Christian and Krauss, Falk Thorsten and Valdes Landa, Jesus Eduardo
    and Pantenburg, Isabel and Roling, Bernhard and Bund, Andreas}, year={2025} }'
  chicago: 'Stich, Michael, Christian Leppin, Falk Thorsten Krauss, Jesus Eduardo
    Valdes Landa, Isabel Pantenburg, Bernhard Roling, and Andreas Bund. “Comparing
    the SEI Formation on Copper and Amorphous Carbon: A Study with Combined Operando
    Methods.” <i>Batteries</i> 11, no. 7 (2025). <a href="https://doi.org/10.3390/batteries11070273">https://doi.org/10.3390/batteries11070273</a>.'
  ieee: 'M. Stich <i>et al.</i>, “Comparing the SEI Formation on Copper and Amorphous
    Carbon: A Study with Combined Operando Methods,” <i>Batteries</i>, vol. 11, no.
    7, Art. no. 273, 2025, doi: <a href="https://doi.org/10.3390/batteries11070273">10.3390/batteries11070273</a>.'
  mla: 'Stich, Michael, et al. “Comparing the SEI Formation on Copper and Amorphous
    Carbon: A Study with Combined Operando Methods.” <i>Batteries</i>, vol. 11, no.
    7, 273, MDPI AG, 2025, doi:<a href="https://doi.org/10.3390/batteries11070273">10.3390/batteries11070273</a>.'
  short: M. Stich, C. Leppin, F.T. Krauss, J.E. Valdes Landa, I. Pantenburg, B. Roling,
    A. Bund, Batteries 11 (2025).
date_created: 2025-12-18T16:56:12Z
date_updated: 2025-12-18T17:47:08Z
doi: 10.3390/batteries11070273
extern: '1'
intvolume: '        11'
issue: '7'
language:
- iso: eng
publication: Batteries
publication_identifier:
  issn:
  - 2313-0105
publication_status: published
publisher: MDPI AG
quality_controlled: '1'
status: public
title: 'Comparing the SEI Formation on Copper and Amorphous Carbon: A Study with Combined
  Operando Methods'
type: journal_article
user_id: '117722'
volume: 11
year: '2025'
...
---
_id: '63224'
abstract:
- lang: eng
  text: <jats:p>By monitoring the solidification of droplets of plant latices with
    a fast quartz crystal microbalance with dissipation monitoring (QCM-D), droplets
    from Campanula glomerata were found to solidify much faster than droplets from
    Euphorbia characias and also faster than droplets from all technical latices tested.
    A similar conclusion was drawn from optical videos, where the plants were injured
    and the milky fluid was stretched (sometimes forming fibers) after the cut. Rapid
    solidification cannot be explained with physical drying because physical drying
    is transport-limited and therefore is inherently slow. It can, however, be explained
    with coagulation being triggered by a sudden decrease in hydrostatic pressure.
    A mechanism based on a pressure drop is corroborated by optical videos of both
    plants being injured under water. While the liquid exuded by E. characias keeps
    streaming away, the liquid exuded by C. glomerata quickly forms a plug even under
    water. Presumably, the pressure drop causes an influx of serum into the laticifers.
    The serum, in turn, triggers a transition from a liquid–liquid phase separated
    state (an LLPS state) of a resin and hardener to a single-phase state. QCM measurements,
    optical videos, and cryo-SEM images suggest that LLPS plays a role in the solidification
    of C. glomerata.</jats:p>
article_number: '798'
article_type: original
author:
- first_name: Arne
  full_name: Langhoff, Arne
  last_name: Langhoff
- first_name: Astrid
  full_name: Peschel, Astrid
  last_name: Peschel
- first_name: Christian
  full_name: Leppin, Christian
  id: '117722'
  last_name: Leppin
- first_name: Sebastian
  full_name: Kruppert, Sebastian
  last_name: Kruppert
- first_name: Thomas
  full_name: Speck, Thomas
  last_name: Speck
- first_name: Diethelm
  full_name: Johannsmann, Diethelm
  last_name: Johannsmann
citation:
  ama: Langhoff A, Peschel A, Leppin C, Kruppert S, Speck T, Johannsmann D. Rapid
    Solidification of Plant Latices from Campanula glomerata Driven by a Sudden Decrease
    in Hydrostatic Pressure. <i>Plants</i>. 2025;14(5). doi:<a href="https://doi.org/10.3390/plants14050798">10.3390/plants14050798</a>
  apa: Langhoff, A., Peschel, A., Leppin, C., Kruppert, S., Speck, T., &#38; Johannsmann,
    D. (2025). Rapid Solidification of Plant Latices from Campanula glomerata Driven
    by a Sudden Decrease in Hydrostatic Pressure. <i>Plants</i>, <i>14</i>(5), Article
    798. <a href="https://doi.org/10.3390/plants14050798">https://doi.org/10.3390/plants14050798</a>
  bibtex: '@article{Langhoff_Peschel_Leppin_Kruppert_Speck_Johannsmann_2025, title={Rapid
    Solidification of Plant Latices from Campanula glomerata Driven by a Sudden Decrease
    in Hydrostatic Pressure}, volume={14}, DOI={<a href="https://doi.org/10.3390/plants14050798">10.3390/plants14050798</a>},
    number={5798}, journal={Plants}, publisher={MDPI AG}, author={Langhoff, Arne and
    Peschel, Astrid and Leppin, Christian and Kruppert, Sebastian and Speck, Thomas
    and Johannsmann, Diethelm}, year={2025} }'
  chicago: Langhoff, Arne, Astrid Peschel, Christian Leppin, Sebastian Kruppert, Thomas
    Speck, and Diethelm Johannsmann. “Rapid Solidification of Plant Latices from Campanula
    Glomerata Driven by a Sudden Decrease in Hydrostatic Pressure.” <i>Plants</i>
    14, no. 5 (2025). <a href="https://doi.org/10.3390/plants14050798">https://doi.org/10.3390/plants14050798</a>.
  ieee: 'A. Langhoff, A. Peschel, C. Leppin, S. Kruppert, T. Speck, and D. Johannsmann,
    “Rapid Solidification of Plant Latices from Campanula glomerata Driven by a Sudden
    Decrease in Hydrostatic Pressure,” <i>Plants</i>, vol. 14, no. 5, Art. no. 798,
    2025, doi: <a href="https://doi.org/10.3390/plants14050798">10.3390/plants14050798</a>.'
  mla: Langhoff, Arne, et al. “Rapid Solidification of Plant Latices from Campanula
    Glomerata Driven by a Sudden Decrease in Hydrostatic Pressure.” <i>Plants</i>,
    vol. 14, no. 5, 798, MDPI AG, 2025, doi:<a href="https://doi.org/10.3390/plants14050798">10.3390/plants14050798</a>.
  short: A. Langhoff, A. Peschel, C. Leppin, S. Kruppert, T. Speck, D. Johannsmann,
    Plants 14 (2025).
date_created: 2025-12-18T16:58:15Z
date_updated: 2025-12-18T17:41:57Z
doi: 10.3390/plants14050798
extern: '1'
intvolume: '        14'
issue: '5'
language:
- iso: eng
publication: Plants
publication_identifier:
  issn:
  - 2223-7747
publication_status: published
publisher: MDPI AG
status: public
title: Rapid Solidification of Plant Latices from Campanula glomerata Driven by a
  Sudden Decrease in Hydrostatic Pressure
type: journal_article
user_id: '117722'
volume: 14
year: '2025'
...
---
_id: '63225'
abstract:
- lang: eng
  text: Various polycations and polyanions were sequentially adsorbed onto the gold
    electrode of a quartz crystal microbalance with dissipation monitoring. The study
    focused on determining the adsorption kinetics, viscoelastic properties, and electroresponsivity
    of polyelectrolyte layers. For the first time, it was demonstrated that the structure
    (compact or expanded) of the layers can be determined by electroresponsivity.
    Viscoelastic modeling alone did not provide a conclusive answer as to whether
    the layers were compact or expanded. The study was further enriched by streaming
    potential and contact angle measurements, where polyelectrolyte multilayers were
    formed on mica. It was found that successive adsorption of layers led to periodic
    inversion of the zeta potential. Systematic differences were observed between
    the different top layers, which were explained by intermixing between layers.
    The presence or absence of interpenetration, as determined by the measurements
    of streaming potential and contact angles, correlated well with electroresponsivity.
article_type: original
author:
- first_name: Christian
  full_name: Leppin, Christian
  id: '117722'
  last_name: Leppin
- first_name: Agata
  full_name: Pomorska, Agata
  last_name: Pomorska
- first_name: Maria
  full_name: Morga, Maria
  last_name: Morga
- first_name: Pawel
  full_name: Pomastowski, Pawel
  last_name: Pomastowski
- first_name: Piotr
  full_name: Fijałkowski, Piotr
  last_name: Fijałkowski
- first_name: Aneta
  full_name: Michna, Aneta
  last_name: Michna
- first_name: Diethelm
  full_name: Johannsmann, Diethelm
  last_name: Johannsmann
citation:
  ama: Leppin C, Pomorska A, Morga M, et al. Swelling Degree of Polyelectrolyte Layers
    Determined by an Electrochemical Quartz Crystal Microbalance. <i>Biomacromolecules</i>.
    2025;26(2):914-928. doi:<a href="https://doi.org/10.1021/acs.biomac.4c01205">10.1021/acs.biomac.4c01205</a>
  apa: Leppin, C., Pomorska, A., Morga, M., Pomastowski, P., Fijałkowski, P., Michna,
    A., &#38; Johannsmann, D. (2025). Swelling Degree of Polyelectrolyte Layers Determined
    by an Electrochemical Quartz Crystal Microbalance. <i>Biomacromolecules</i>, <i>26</i>(2),
    914–928. <a href="https://doi.org/10.1021/acs.biomac.4c01205">https://doi.org/10.1021/acs.biomac.4c01205</a>
  bibtex: '@article{Leppin_Pomorska_Morga_Pomastowski_Fijałkowski_Michna_Johannsmann_2025,
    title={Swelling Degree of Polyelectrolyte Layers Determined by an Electrochemical
    Quartz Crystal Microbalance}, volume={26}, DOI={<a href="https://doi.org/10.1021/acs.biomac.4c01205">10.1021/acs.biomac.4c01205</a>},
    number={2}, journal={Biomacromolecules}, publisher={American Chemical Society
    (ACS)}, author={Leppin, Christian and Pomorska, Agata and Morga, Maria and Pomastowski,
    Pawel and Fijałkowski, Piotr and Michna, Aneta and Johannsmann, Diethelm}, year={2025},
    pages={914–928} }'
  chicago: 'Leppin, Christian, Agata Pomorska, Maria Morga, Pawel Pomastowski, Piotr
    Fijałkowski, Aneta Michna, and Diethelm Johannsmann. “Swelling Degree of Polyelectrolyte
    Layers Determined by an Electrochemical Quartz Crystal Microbalance.” <i>Biomacromolecules</i>
    26, no. 2 (2025): 914–28. <a href="https://doi.org/10.1021/acs.biomac.4c01205">https://doi.org/10.1021/acs.biomac.4c01205</a>.'
  ieee: 'C. Leppin <i>et al.</i>, “Swelling Degree of Polyelectrolyte Layers Determined
    by an Electrochemical Quartz Crystal Microbalance,” <i>Biomacromolecules</i>,
    vol. 26, no. 2, pp. 914–928, 2025, doi: <a href="https://doi.org/10.1021/acs.biomac.4c01205">10.1021/acs.biomac.4c01205</a>.'
  mla: Leppin, Christian, et al. “Swelling Degree of Polyelectrolyte Layers Determined
    by an Electrochemical Quartz Crystal Microbalance.” <i>Biomacromolecules</i>,
    vol. 26, no. 2, American Chemical Society (ACS), 2025, pp. 914–28, doi:<a href="https://doi.org/10.1021/acs.biomac.4c01205">10.1021/acs.biomac.4c01205</a>.
  short: C. Leppin, A. Pomorska, M. Morga, P. Pomastowski, P. Fijałkowski, A. Michna,
    D. Johannsmann, Biomacromolecules 26 (2025) 914–928.
date_created: 2025-12-18T16:59:12Z
date_updated: 2025-12-18T17:44:44Z
doi: 10.1021/acs.biomac.4c01205
extern: '1'
intvolume: '        26'
issue: '2'
language:
- iso: eng
page: 914-928
publication: Biomacromolecules
publication_identifier:
  issn:
  - 1525-7797
  - 1526-4602
publication_status: published
publisher: American Chemical Society (ACS)
status: public
title: Swelling Degree of Polyelectrolyte Layers Determined by an Electrochemical
  Quartz Crystal Microbalance
type: journal_article
user_id: '117722'
volume: 26
year: '2025'
...
---
_id: '63226'
abstract:
- lang: eng
  text: <jats:p>Nanobubbles in water splitting are recognized by the EQCM-D. They
    are ubiquitous. Lifetimes are in the range of seconds.</jats:p>
article_type: original
author:
- first_name: Christian
  full_name: Leppin, Christian
  id: '117722'
  last_name: Leppin
- first_name: Arne
  full_name: Langhoff, Arne
  last_name: Langhoff
- first_name: Diethelm
  full_name: Johannsmann, Diethelm
  last_name: Johannsmann
citation:
  ama: Leppin C, Langhoff A, Johannsmann D. A fast electrochemical quartz crystal
    microbalance (EQCM) evidences the presence of nanobubbles in alkaline water splitting.
    <i>Physical Chemistry Chemical Physics</i>. 2025;27(37):19733-19747. doi:<a href="https://doi.org/10.1039/d5cp02691a">10.1039/d5cp02691a</a>
  apa: Leppin, C., Langhoff, A., &#38; Johannsmann, D. (2025). A fast electrochemical
    quartz crystal microbalance (EQCM) evidences the presence of nanobubbles in alkaline
    water splitting. <i>Physical Chemistry Chemical Physics</i>, <i>27</i>(37), 19733–19747.
    <a href="https://doi.org/10.1039/d5cp02691a">https://doi.org/10.1039/d5cp02691a</a>
  bibtex: '@article{Leppin_Langhoff_Johannsmann_2025, title={A fast electrochemical
    quartz crystal microbalance (EQCM) evidences the presence of nanobubbles in alkaline
    water splitting}, volume={27}, DOI={<a href="https://doi.org/10.1039/d5cp02691a">10.1039/d5cp02691a</a>},
    number={37}, journal={Physical Chemistry Chemical Physics}, publisher={Royal Society
    of Chemistry (RSC)}, author={Leppin, Christian and Langhoff, Arne and Johannsmann,
    Diethelm}, year={2025}, pages={19733–19747} }'
  chicago: 'Leppin, Christian, Arne Langhoff, and Diethelm Johannsmann. “A Fast Electrochemical
    Quartz Crystal Microbalance (EQCM) Evidences the Presence of Nanobubbles in Alkaline
    Water Splitting.” <i>Physical Chemistry Chemical Physics</i> 27, no. 37 (2025):
    19733–47. <a href="https://doi.org/10.1039/d5cp02691a">https://doi.org/10.1039/d5cp02691a</a>.'
  ieee: 'C. Leppin, A. Langhoff, and D. Johannsmann, “A fast electrochemical quartz
    crystal microbalance (EQCM) evidences the presence of nanobubbles in alkaline
    water splitting,” <i>Physical Chemistry Chemical Physics</i>, vol. 27, no. 37,
    pp. 19733–19747, 2025, doi: <a href="https://doi.org/10.1039/d5cp02691a">10.1039/d5cp02691a</a>.'
  mla: Leppin, Christian, et al. “A Fast Electrochemical Quartz Crystal Microbalance
    (EQCM) Evidences the Presence of Nanobubbles in Alkaline Water Splitting.” <i>Physical
    Chemistry Chemical Physics</i>, vol. 27, no. 37, Royal Society of Chemistry (RSC),
    2025, pp. 19733–47, doi:<a href="https://doi.org/10.1039/d5cp02691a">10.1039/d5cp02691a</a>.
  short: C. Leppin, A. Langhoff, D. Johannsmann, Physical Chemistry Chemical Physics
    27 (2025) 19733–19747.
date_created: 2025-12-18T17:00:11Z
date_updated: 2025-12-18T17:43:25Z
doi: 10.1039/d5cp02691a
extern: '1'
intvolume: '        27'
issue: '37'
language:
- iso: eng
page: 19733-19747
publication: Physical Chemistry Chemical Physics
publication_identifier:
  issn:
  - 1463-9076
  - 1463-9084
publication_status: published
publisher: Royal Society of Chemistry (RSC)
status: public
title: A fast electrochemical quartz crystal microbalance (EQCM) evidences the presence
  of nanobubbles in alkaline water splitting
type: journal_article
user_id: '117722'
volume: 27
year: '2025'
...
---
_id: '63241'
author:
- first_name: Lena Katharina
  full_name: Schmitt-Richter, Lena Katharina
  last_name: Schmitt-Richter
- first_name: Sabrina
  full_name: Wüllner, Sabrina
  id: '105046'
  last_name: Wüllner
- first_name: Katharina
  full_name: Schmidt, Katharina
  last_name: Schmidt
- first_name: Muna
  full_name: Ebeling, Muna
  last_name: Ebeling
citation:
  ama: Schmitt-Richter LK, Wüllner S, Schmidt K, Ebeling M. Von der Idee zur Umsetzung
    – Der Schulversuch an der Maria-Montessori-Gesamtschule in Düsseldorf. <i>Pädagogikunterricht
    Die Fachzeitschrift für die pädagogische Fächergruppe</i>. 2025;45(4):65-70.
  apa: Schmitt-Richter, L. K., Wüllner, S., Schmidt, K., &#38; Ebeling, M. (2025).
    Von der Idee zur Umsetzung – Der Schulversuch an der Maria-Montessori-Gesamtschule
    in Düsseldorf. <i>Pädagogikunterricht. Die Fachzeitschrift Für Die Pädagogische
    Fächergruppe.</i>, <i>45</i>(4), 65–70.
  bibtex: '@article{Schmitt-Richter_Wüllner_Schmidt_Ebeling_2025, title={Von der Idee
    zur Umsetzung – Der Schulversuch an der Maria-Montessori-Gesamtschule in Düsseldorf},
    volume={45}, number={4}, journal={Pädagogikunterricht. Die Fachzeitschrift für
    die pädagogische Fächergruppe.}, author={Schmitt-Richter, Lena Katharina and Wüllner,
    Sabrina and Schmidt, Katharina and Ebeling, Muna}, year={2025}, pages={65–70}
    }'
  chicago: 'Schmitt-Richter, Lena Katharina, Sabrina Wüllner, Katharina Schmidt, and
    Muna Ebeling. “Von Der Idee Zur Umsetzung – Der Schulversuch an Der Maria-Montessori-Gesamtschule
    in Düsseldorf.” <i>Pädagogikunterricht. Die Fachzeitschrift Für Die Pädagogische
    Fächergruppe.</i> 45, no. 4 (2025): 65–70.'
  ieee: L. K. Schmitt-Richter, S. Wüllner, K. Schmidt, and M. Ebeling, “Von der Idee
    zur Umsetzung – Der Schulversuch an der Maria-Montessori-Gesamtschule in Düsseldorf,”
    <i>Pädagogikunterricht. Die Fachzeitschrift für die pädagogische Fächergruppe.</i>,
    vol. 45, no. 4, pp. 65–70, 2025.
  mla: Schmitt-Richter, Lena Katharina, et al. “Von Der Idee Zur Umsetzung – Der Schulversuch
    an Der Maria-Montessori-Gesamtschule in Düsseldorf.” <i>Pädagogikunterricht. Die
    Fachzeitschrift Für Die Pädagogische Fächergruppe.</i>, vol. 45, no. 4, 2025,
    pp. 65–70.
  short: L.K. Schmitt-Richter, S. Wüllner, K. Schmidt, M. Ebeling, Pädagogikunterricht.
    Die Fachzeitschrift Für Die Pädagogische Fächergruppe. 45 (2025) 65–70.
date_created: 2025-12-18T18:38:06Z
date_updated: 2025-12-18T18:42:16Z
intvolume: '        45'
issue: '4'
language:
- iso: eng
page: 65-70
publication: Pädagogikunterricht. Die Fachzeitschrift für die pädagogische Fächergruppe.
status: public
title: Von der Idee zur Umsetzung – Der Schulversuch an der Maria-Montessori-Gesamtschule
  in Düsseldorf
type: journal_article
user_id: '105046'
volume: 45
year: '2025'
...
---
_id: '63250'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n                  <jats:p>\r\n                    An
    initial-boundary value problem for\r\n                    <jats:disp-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$\\begin{aligned}
    \\left\\{ \\begin{array}{ll}u_{tt} = \\big (\\gamma (\\Theta ) u_{xt}\\big )_x
    + au_{xx} - \\big (f(\\Theta )\\big )_x, \\qquad &amp;  x\\in \\Omega , \\ t&gt;0,
    \\\\[1mm] \\Theta _t = \\Theta _{xx} + \\gamma (\\Theta ) u_{xt}^2 - f(\\Theta
    ) u_{xt}, \\qquad &amp;  x\\in \\Omega , \\ t&gt;0, \\end{array} \\right. \\end{aligned}$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mtable>\r\n
    \                             <mml:mtr>\r\n                                <mml:mtd>\r\n
    \                                 <mml:mfenced>\r\n                                    <mml:mrow>\r\n
    \                                     <mml:mtable>\r\n                                        <mml:mtr>\r\n
    \                                         <mml:mtd>\r\n                                            <mml:mrow>\r\n
    \                                             <mml:msub>\r\n                                                <mml:mi>u</mml:mi>\r\n
    \                                               <mml:mrow>\r\n                                                  <mml:mi>tt</mml:mi>\r\n
    \                                               </mml:mrow>\r\n                                              </mml:msub>\r\n
    \                                             <mml:mo>=</mml:mo>\r\n                                              <mml:mrow>\r\n
    \                                               <mml:mo>(</mml:mo>\r\n                                              </mml:mrow>\r\n
    \                                             <mml:mi>γ</mml:mi>\r\n                                              <mml:mrow>\r\n
    \                                               <mml:mo>(</mml:mo>\r\n                                                <mml:mi>Θ</mml:mi>\r\n
    \                                               <mml:mo>)</mml:mo>\r\n                                              </mml:mrow>\r\n
    \                                             <mml:msub>\r\n                                                <mml:mi>u</mml:mi>\r\n
    \                                               <mml:mrow>\r\n                                                  <mml:mi>xt</mml:mi>\r\n
    \                                               </mml:mrow>\r\n                                              </mml:msub>\r\n
    \                                             <mml:msub>\r\n                                                <mml:mrow>\r\n
    \                                                 <mml:mo>)</mml:mo>\r\n                                                </mml:mrow>\r\n
    \                                               <mml:mi>x</mml:mi>\r\n                                              </mml:msub>\r\n
    \                                             <mml:mo>+</mml:mo>\r\n                                              <mml:mi>a</mml:mi>\r\n
    \                                             <mml:msub>\r\n                                                <mml:mi>u</mml:mi>\r\n
    \                                               <mml:mrow>\r\n                                                  <mml:mi>xx</mml:mi>\r\n
    \                                               </mml:mrow>\r\n                                              </mml:msub>\r\n
    \                                             <mml:mo>-</mml:mo>\r\n                                              <mml:mrow>\r\n
    \                                               <mml:mo>(</mml:mo>\r\n                                              </mml:mrow>\r\n
    \                                             <mml:mi>f</mml:mi>\r\n                                              <mml:mrow>\r\n
    \                                               <mml:mo>(</mml:mo>\r\n                                                <mml:mi>Θ</mml:mi>\r\n
    \                                               <mml:mo>)</mml:mo>\r\n                                              </mml:mrow>\r\n
    \                                             <mml:msub>\r\n                                                <mml:mrow>\r\n
    \                                                 <mml:mo>)</mml:mo>\r\n                                                </mml:mrow>\r\n
    \                                               <mml:mi>x</mml:mi>\r\n                                              </mml:msub>\r\n
    \                                             <mml:mo>,</mml:mo>\r\n                                              <mml:mspace/>\r\n
    \                                           </mml:mrow>\r\n                                          </mml:mtd>\r\n
    \                                         <mml:mtd>\r\n                                            <mml:mrow>\r\n
    \                                             <mml:mi>x</mml:mi>\r\n                                              <mml:mo>∈</mml:mo>\r\n
    \                                             <mml:mi>Ω</mml:mi>\r\n                                              <mml:mo>,</mml:mo>\r\n
    \                                             <mml:mspace/>\r\n                                              <mml:mi>t</mml:mi>\r\n
    \                                             <mml:mo>&gt;</mml:mo>\r\n                                              <mml:mn>0</mml:mn>\r\n
    \                                             <mml:mo>,</mml:mo>\r\n                                            </mml:mrow>\r\n
    \                                         </mml:mtd>\r\n                                        </mml:mtr>\r\n
    \                                       <mml:mtr>\r\n                                          <mml:mtd>\r\n
    \                                           <mml:mrow>\r\n                                              <mml:mrow/>\r\n
    \                                             <mml:mrow>\r\n                                                <mml:mo>[</mml:mo>\r\n
    \                                               <mml:mn>1</mml:mn>\r\n                                                <mml:mi>m</mml:mi>\r\n
    \                                               <mml:mi>m</mml:mi>\r\n                                                <mml:mo>]</mml:mo>\r\n
    \                                             </mml:mrow>\r\n                                              <mml:msub>\r\n
    \                                               <mml:mi>Θ</mml:mi>\r\n                                                <mml:mi>t</mml:mi>\r\n
    \                                             </mml:msub>\r\n                                              <mml:mo>=</mml:mo>\r\n
    \                                             <mml:msub>\r\n                                                <mml:mi>Θ</mml:mi>\r\n
    \                                               <mml:mrow>\r\n                                                  <mml:mi>xx</mml:mi>\r\n
    \                                               </mml:mrow>\r\n                                              </mml:msub>\r\n
    \                                             <mml:mo>+</mml:mo>\r\n                                              <mml:mi>γ</mml:mi>\r\n
    \                                             <mml:mrow>\r\n                                                <mml:mo>(</mml:mo>\r\n
    \                                               <mml:mi>Θ</mml:mi>\r\n                                                <mml:mo>)</mml:mo>\r\n
    \                                             </mml:mrow>\r\n                                              <mml:msubsup>\r\n
    \                                               <mml:mi>u</mml:mi>\r\n                                                <mml:mrow>\r\n
    \                                                 <mml:mi>xt</mml:mi>\r\n                                                </mml:mrow>\r\n
    \                                               <mml:mn>2</mml:mn>\r\n                                              </mml:msubsup>\r\n
    \                                             <mml:mo>-</mml:mo>\r\n                                              <mml:mi>f</mml:mi>\r\n
    \                                             <mml:mrow>\r\n                                                <mml:mo>(</mml:mo>\r\n
    \                                               <mml:mi>Θ</mml:mi>\r\n                                                <mml:mo>)</mml:mo>\r\n
    \                                             </mml:mrow>\r\n                                              <mml:msub>\r\n
    \                                               <mml:mi>u</mml:mi>\r\n                                                <mml:mrow>\r\n
    \                                                 <mml:mi>xt</mml:mi>\r\n                                                </mml:mrow>\r\n
    \                                             </mml:msub>\r\n                                              <mml:mo>,</mml:mo>\r\n
    \                                             <mml:mspace/>\r\n                                            </mml:mrow>\r\n
    \                                         </mml:mtd>\r\n                                          <mml:mtd>\r\n
    \                                           <mml:mrow>\r\n                                              <mml:mi>x</mml:mi>\r\n
    \                                             <mml:mo>∈</mml:mo>\r\n                                              <mml:mi>Ω</mml:mi>\r\n
    \                                             <mml:mo>,</mml:mo>\r\n                                              <mml:mspace/>\r\n
    \                                             <mml:mi>t</mml:mi>\r\n                                              <mml:mo>&gt;</mml:mo>\r\n
    \                                             <mml:mn>0</mml:mn>\r\n                                              <mml:mo>,</mml:mo>\r\n
    \                                           </mml:mrow>\r\n                                          </mml:mtd>\r\n
    \                                       </mml:mtr>\r\n                                      </mml:mtable>\r\n
    \                                   </mml:mrow>\r\n                                  </mml:mfenced>\r\n
    \                               </mml:mtd>\r\n                              </mml:mtr>\r\n
    \                           </mml:mtable>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:disp-formula>\r\n                    is considered
    in an open bounded real interval\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$\\Omega
    $$</jats:tex-math>\r\n                        <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mi>Ω</mml:mi>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   . Under the assumption that\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$\\gamma
    \\in C^0([0,\\infty ))$$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:mi>γ</mml:mi>\r\n                            <mml:mo>∈</mml:mo>\r\n
    \                           <mml:msup>\r\n                              <mml:mi>C</mml:mi>\r\n
    \                             <mml:mn>0</mml:mn>\r\n                            </mml:msup>\r\n
    \                           <mml:mrow>\r\n                              <mml:mo>(</mml:mo>\r\n
    \                             <mml:mrow>\r\n                                <mml:mo>[</mml:mo>\r\n
    \                               <mml:mn>0</mml:mn>\r\n                                <mml:mo>,</mml:mo>\r\n
    \                               <mml:mi>∞</mml:mi>\r\n                                <mml:mo>)</mml:mo>\r\n
    \                             </mml:mrow>\r\n                              <mml:mo>)</mml:mo>\r\n
    \                           </mml:mrow>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    and\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$f\\in
    C^0([0,\\infty ))$$</jats:tex-math>\r\n                        <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mi>f</mml:mi>\r\n
    \                           <mml:mo>∈</mml:mo>\r\n                            <mml:msup>\r\n
    \                             <mml:mi>C</mml:mi>\r\n                              <mml:mn>0</mml:mn>\r\n
    \                           </mml:msup>\r\n                            <mml:mrow>\r\n
    \                             <mml:mo>(</mml:mo>\r\n                              <mml:mrow>\r\n
    \                               <mml:mo>[</mml:mo>\r\n                                <mml:mn>0</mml:mn>\r\n
    \                               <mml:mo>,</mml:mo>\r\n                                <mml:mi>∞</mml:mi>\r\n
    \                               <mml:mo>)</mml:mo>\r\n                              </mml:mrow>\r\n
    \                             <mml:mo>)</mml:mo>\r\n                            </mml:mrow>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   are such that\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$f(0)=0$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mi>f</mml:mi>\r\n
    \                           <mml:mo>(</mml:mo>\r\n                            <mml:mn>0</mml:mn>\r\n
    \                           <mml:mo>)</mml:mo>\r\n                            <mml:mo>=</mml:mo>\r\n
    \                           <mml:mn>0</mml:mn>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    , and\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$k_\\gamma
    \\le \\gamma \\le K_\\gamma $$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:msub>\r\n                              <mml:mi>k</mml:mi>\r\n
    \                             <mml:mi>γ</mml:mi>\r\n                            </mml:msub>\r\n
    \                           <mml:mo>≤</mml:mo>\r\n                            <mml:mi>γ</mml:mi>\r\n
    \                           <mml:mo>≤</mml:mo>\r\n                            <mml:msub>\r\n
    \                             <mml:mi>K</mml:mi>\r\n                              <mml:mi>γ</mml:mi>\r\n
    \                           </mml:msub>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    as well as\r\n
    \                   <jats:disp-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$\\begin{aligned} |f(\\xi )| \\le K_f
    \\cdot (\\xi +1)^\\alpha \\qquad \\hbox {for all } \\xi \\ge 0 \\end{aligned}$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mtable>\r\n
    \                             <mml:mtr>\r\n                                <mml:mtd>\r\n
    \                                 <mml:mrow>\r\n                                    <mml:mrow>\r\n
    \                                     <mml:mo>|</mml:mo>\r\n                                      <mml:mi>f</mml:mi>\r\n
    \                                     <mml:mrow>\r\n                                        <mml:mo>(</mml:mo>\r\n
    \                                       <mml:mi>ξ</mml:mi>\r\n                                        <mml:mo>)</mml:mo>\r\n
    \                                     </mml:mrow>\r\n                                      <mml:mo>|</mml:mo>\r\n
    \                                   </mml:mrow>\r\n                                    <mml:mo>≤</mml:mo>\r\n
    \                                   <mml:msub>\r\n                                      <mml:mi>K</mml:mi>\r\n
    \                                     <mml:mi>f</mml:mi>\r\n                                    </mml:msub>\r\n
    \                                   <mml:mo>·</mml:mo>\r\n                                    <mml:msup>\r\n
    \                                     <mml:mrow>\r\n                                        <mml:mo>(</mml:mo>\r\n
    \                                       <mml:mi>ξ</mml:mi>\r\n                                        <mml:mo>+</mml:mo>\r\n
    \                                       <mml:mn>1</mml:mn>\r\n                                        <mml:mo>)</mml:mo>\r\n
    \                                     </mml:mrow>\r\n                                      <mml:mi>α</mml:mi>\r\n
    \                                   </mml:msup>\r\n                                    <mml:mspace/>\r\n
    \                                   <mml:mtext>for all</mml:mtext>\r\n                                    <mml:mspace/>\r\n
    \                                   <mml:mi>ξ</mml:mi>\r\n                                    <mml:mo>≥</mml:mo>\r\n
    \                                   <mml:mn>0</mml:mn>\r\n                                  </mml:mrow>\r\n
    \                               </mml:mtd>\r\n                              </mml:mtr>\r\n
    \                           </mml:mtable>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:disp-formula>\r\n                    with some\r\n
    \                   <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$k_\\gamma&gt;0, K_\\gamma&gt;0, K_f&gt;0$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:msub>\r\n
    \                             <mml:mi>k</mml:mi>\r\n                              <mml:mi>γ</mml:mi>\r\n
    \                           </mml:msub>\r\n                            <mml:mo>&gt;</mml:mo>\r\n
    \                           <mml:mn>0</mml:mn>\r\n                            <mml:mo>,</mml:mo>\r\n
    \                           <mml:msub>\r\n                              <mml:mi>K</mml:mi>\r\n
    \                             <mml:mi>γ</mml:mi>\r\n                            </mml:msub>\r\n
    \                           <mml:mo>&gt;</mml:mo>\r\n                            <mml:mn>0</mml:mn>\r\n
    \                           <mml:mo>,</mml:mo>\r\n                            <mml:msub>\r\n
    \                             <mml:mi>K</mml:mi>\r\n                              <mml:mi>f</mml:mi>\r\n
    \                           </mml:msub>\r\n                            <mml:mo>&gt;</mml:mo>\r\n
    \                           <mml:mn>0</mml:mn>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    and\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$\\alpha
    &lt;\\frac{3}{2}$$</jats:tex-math>\r\n                        <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mi>α</mml:mi>\r\n
    \                           <mml:mo>&lt;</mml:mo>\r\n                            <mml:mfrac>\r\n
    \                             <mml:mn>3</mml:mn>\r\n                              <mml:mn>2</mml:mn>\r\n
    \                           </mml:mfrac>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    , for all suitably
    regular initial data of arbitrary size a statement on global existence of a global
    weak solution is derived. By particularly covering the thermodynamically consistent
    choice\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$f\\equiv id$$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:mi>f</mml:mi>\r\n                            <mml:mo>≡</mml:mo>\r\n
    \                           <mml:mi>i</mml:mi>\r\n                            <mml:mi>d</mml:mi>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   of predominant physical relevance, this appears to go beyond
    previous related literature which seems to either rely on independence of\r\n
    \                   <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$\\gamma $$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mi>γ</mml:mi>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    on\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$\\Theta
    $$</jats:tex-math>\r\n                        <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mi>Θ</mml:mi>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   , or to operate on finite time intervals.\r\n                  </jats:p>"
article_number: '192'
author:
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Winkler M. Large-data solutions in one-dimensional thermoviscoelasticity involving
    temperature-dependent viscosities. <i>Zeitschrift für angewandte Mathematik und
    Physik</i>. 2025;76(5). doi:<a href="https://doi.org/10.1007/s00033-025-02582-y">10.1007/s00033-025-02582-y</a>
  apa: Winkler, M. (2025). Large-data solutions in one-dimensional thermoviscoelasticity
    involving temperature-dependent viscosities. <i>Zeitschrift Für Angewandte Mathematik
    Und Physik</i>, <i>76</i>(5), Article 192. <a href="https://doi.org/10.1007/s00033-025-02582-y">https://doi.org/10.1007/s00033-025-02582-y</a>
  bibtex: '@article{Winkler_2025, title={Large-data solutions in one-dimensional thermoviscoelasticity
    involving temperature-dependent viscosities}, volume={76}, DOI={<a href="https://doi.org/10.1007/s00033-025-02582-y">10.1007/s00033-025-02582-y</a>},
    number={5192}, journal={Zeitschrift für angewandte Mathematik und Physik}, publisher={Springer
    Science and Business Media LLC}, author={Winkler, Michael}, year={2025} }'
  chicago: Winkler, Michael. “Large-Data Solutions in One-Dimensional Thermoviscoelasticity
    Involving Temperature-Dependent Viscosities.” <i>Zeitschrift Für Angewandte Mathematik
    Und Physik</i> 76, no. 5 (2025). <a href="https://doi.org/10.1007/s00033-025-02582-y">https://doi.org/10.1007/s00033-025-02582-y</a>.
  ieee: 'M. Winkler, “Large-data solutions in one-dimensional thermoviscoelasticity
    involving temperature-dependent viscosities,” <i>Zeitschrift für angewandte Mathematik
    und Physik</i>, vol. 76, no. 5, Art. no. 192, 2025, doi: <a href="https://doi.org/10.1007/s00033-025-02582-y">10.1007/s00033-025-02582-y</a>.'
  mla: Winkler, Michael. “Large-Data Solutions in One-Dimensional Thermoviscoelasticity
    Involving Temperature-Dependent Viscosities.” <i>Zeitschrift Für Angewandte Mathematik
    Und Physik</i>, vol. 76, no. 5, 192, Springer Science and Business Media LLC,
    2025, doi:<a href="https://doi.org/10.1007/s00033-025-02582-y">10.1007/s00033-025-02582-y</a>.
  short: M. Winkler, Zeitschrift Für Angewandte Mathematik Und Physik 76 (2025).
date_created: 2025-12-18T19:03:19Z
date_updated: 2025-12-18T20:13:25Z
doi: 10.1007/s00033-025-02582-y
intvolume: '        76'
issue: '5'
language:
- iso: eng
publication: Zeitschrift für angewandte Mathematik und Physik
publication_identifier:
  issn:
  - 0044-2275
  - 1420-9039
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Large-data solutions in one-dimensional thermoviscoelasticity involving temperature-dependent
  viscosities
type: journal_article
user_id: '31496'
volume: 76
year: '2025'
...
---
_id: '63249'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n                  <jats:p>\r\n                    The
    model\r\n                    <jats:disp-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$\\begin{aligned} \\left\\{ \\begin{array}{l}u_{tt}
    = \\big (\\gamma (\\Theta ) u_{xt}\\big )_x + au_{xx} - \\big (f(\\Theta )\\big
    )_x, \\\\[1mm] \\Theta _t = \\Theta _{xx} + \\gamma (\\Theta ) u_{xt}^2 - f(\\Theta
    ) u_{xt}, \\end{array} \\right. \\end{aligned}$$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:mtable>\r\n                              <mml:mtr>\r\n
    \                               <mml:mtd>\r\n                                  <mml:mfenced>\r\n
    \                                   <mml:mrow>\r\n                                      <mml:mtable>\r\n
    \                                       <mml:mtr>\r\n                                          <mml:mtd>\r\n
    \                                           <mml:mrow>\r\n                                              <mml:msub>\r\n
    \                                               <mml:mi>u</mml:mi>\r\n                                                <mml:mrow>\r\n
    \                                                 <mml:mi>tt</mml:mi>\r\n                                                </mml:mrow>\r\n
    \                                             </mml:msub>\r\n                                              <mml:mo>=</mml:mo>\r\n
    \                                             <mml:mrow>\r\n                                                <mml:mo>(</mml:mo>\r\n
    \                                             </mml:mrow>\r\n                                              <mml:mi>γ</mml:mi>\r\n
    \                                             <mml:mrow>\r\n                                                <mml:mo>(</mml:mo>\r\n
    \                                               <mml:mi>Θ</mml:mi>\r\n                                                <mml:mo>)</mml:mo>\r\n
    \                                             </mml:mrow>\r\n                                              <mml:msub>\r\n
    \                                               <mml:mi>u</mml:mi>\r\n                                                <mml:mrow>\r\n
    \                                                 <mml:mi>xt</mml:mi>\r\n                                                </mml:mrow>\r\n
    \                                             </mml:msub>\r\n                                              <mml:msub>\r\n
    \                                               <mml:mrow>\r\n                                                  <mml:mo>)</mml:mo>\r\n
    \                                               </mml:mrow>\r\n                                                <mml:mi>x</mml:mi>\r\n
    \                                             </mml:msub>\r\n                                              <mml:mo>+</mml:mo>\r\n
    \                                             <mml:mi>a</mml:mi>\r\n                                              <mml:msub>\r\n
    \                                               <mml:mi>u</mml:mi>\r\n                                                <mml:mrow>\r\n
    \                                                 <mml:mi>xx</mml:mi>\r\n                                                </mml:mrow>\r\n
    \                                             </mml:msub>\r\n                                              <mml:mo>-</mml:mo>\r\n
    \                                             <mml:mrow>\r\n                                                <mml:mo>(</mml:mo>\r\n
    \                                             </mml:mrow>\r\n                                              <mml:mi>f</mml:mi>\r\n
    \                                             <mml:mrow>\r\n                                                <mml:mo>(</mml:mo>\r\n
    \                                               <mml:mi>Θ</mml:mi>\r\n                                                <mml:mo>)</mml:mo>\r\n
    \                                             </mml:mrow>\r\n                                              <mml:msub>\r\n
    \                                               <mml:mrow>\r\n                                                  <mml:mo>)</mml:mo>\r\n
    \                                               </mml:mrow>\r\n                                                <mml:mi>x</mml:mi>\r\n
    \                                             </mml:msub>\r\n                                              <mml:mo>,</mml:mo>\r\n
    \                                           </mml:mrow>\r\n                                          </mml:mtd>\r\n
    \                                       </mml:mtr>\r\n                                        <mml:mtr>\r\n
    \                                         <mml:mtd>\r\n                                            <mml:mrow>\r\n
    \                                             <mml:mrow/>\r\n                                              <mml:mrow>\r\n
    \                                               <mml:mo>[</mml:mo>\r\n                                                <mml:mn>1</mml:mn>\r\n
    \                                               <mml:mi>m</mml:mi>\r\n                                                <mml:mi>m</mml:mi>\r\n
    \                                               <mml:mo>]</mml:mo>\r\n                                              </mml:mrow>\r\n
    \                                             <mml:msub>\r\n                                                <mml:mi>Θ</mml:mi>\r\n
    \                                               <mml:mi>t</mml:mi>\r\n                                              </mml:msub>\r\n
    \                                             <mml:mo>=</mml:mo>\r\n                                              <mml:msub>\r\n
    \                                               <mml:mi>Θ</mml:mi>\r\n                                                <mml:mrow>\r\n
    \                                                 <mml:mi>xx</mml:mi>\r\n                                                </mml:mrow>\r\n
    \                                             </mml:msub>\r\n                                              <mml:mo>+</mml:mo>\r\n
    \                                             <mml:mi>γ</mml:mi>\r\n                                              <mml:mrow>\r\n
    \                                               <mml:mo>(</mml:mo>\r\n                                                <mml:mi>Θ</mml:mi>\r\n
    \                                               <mml:mo>)</mml:mo>\r\n                                              </mml:mrow>\r\n
    \                                             <mml:msubsup>\r\n                                                <mml:mi>u</mml:mi>\r\n
    \                                               <mml:mrow>\r\n                                                  <mml:mi>xt</mml:mi>\r\n
    \                                               </mml:mrow>\r\n                                                <mml:mn>2</mml:mn>\r\n
    \                                             </mml:msubsup>\r\n                                              <mml:mo>-</mml:mo>\r\n
    \                                             <mml:mi>f</mml:mi>\r\n                                              <mml:mrow>\r\n
    \                                               <mml:mo>(</mml:mo>\r\n                                                <mml:mi>Θ</mml:mi>\r\n
    \                                               <mml:mo>)</mml:mo>\r\n                                              </mml:mrow>\r\n
    \                                             <mml:msub>\r\n                                                <mml:mi>u</mml:mi>\r\n
    \                                               <mml:mrow>\r\n                                                  <mml:mi>xt</mml:mi>\r\n
    \                                               </mml:mrow>\r\n                                              </mml:msub>\r\n
    \                                             <mml:mo>,</mml:mo>\r\n                                            </mml:mrow>\r\n
    \                                         </mml:mtd>\r\n                                        </mml:mtr>\r\n
    \                                     </mml:mtable>\r\n                                    </mml:mrow>\r\n
    \                                 </mml:mfenced>\r\n                                </mml:mtd>\r\n
    \                             </mml:mtr>\r\n                            </mml:mtable>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:disp-formula>\r\n
    \                   for thermoviscoelastic evolution in one-dimensional Kelvin–Voigt
    materials is considered. By means of an approach based on maximal Sobolev regularity
    theory of scalar parabolic equations, it is shown that if\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$\\gamma
    _0&gt;0$$</jats:tex-math>\r\n                        <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:msub>\r\n
    \                             <mml:mi>γ</mml:mi>\r\n                              <mml:mn>0</mml:mn>\r\n
    \                           </mml:msub>\r\n                            <mml:mo>&gt;</mml:mo>\r\n
    \                           <mml:mn>0</mml:mn>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    is fixed, then
    there exists\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$\\delta =\\delta (\\gamma _0)&gt;0$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mi>δ</mml:mi>\r\n
    \                           <mml:mo>=</mml:mo>\r\n                            <mml:mi>δ</mml:mi>\r\n
    \                           <mml:mo>(</mml:mo>\r\n                            <mml:msub>\r\n
    \                             <mml:mi>γ</mml:mi>\r\n                              <mml:mn>0</mml:mn>\r\n
    \                           </mml:msub>\r\n                            <mml:mo>)</mml:mo>\r\n
    \                           <mml:mo>&gt;</mml:mo>\r\n                            <mml:mn>0</mml:mn>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   with the property that for suitably regular initial data of
    arbitrary size an associated initial boundary value problem posed in an open bounded
    interval admits a global classical solution whenever\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$\\gamma
    \\in C^2([0,\\infty ))$$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:mi>γ</mml:mi>\r\n                            <mml:mo>∈</mml:mo>\r\n
    \                           <mml:msup>\r\n                              <mml:mi>C</mml:mi>\r\n
    \                             <mml:mn>2</mml:mn>\r\n                            </mml:msup>\r\n
    \                           <mml:mrow>\r\n                              <mml:mo>(</mml:mo>\r\n
    \                             <mml:mrow>\r\n                                <mml:mo>[</mml:mo>\r\n
    \                               <mml:mn>0</mml:mn>\r\n                                <mml:mo>,</mml:mo>\r\n
    \                               <mml:mi>∞</mml:mi>\r\n                                <mml:mo>)</mml:mo>\r\n
    \                             </mml:mrow>\r\n                              <mml:mo>)</mml:mo>\r\n
    \                           </mml:mrow>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    and\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$f\\in
    C^2([0,\\infty ))$$</jats:tex-math>\r\n                        <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mi>f</mml:mi>\r\n
    \                           <mml:mo>∈</mml:mo>\r\n                            <mml:msup>\r\n
    \                             <mml:mi>C</mml:mi>\r\n                              <mml:mn>2</mml:mn>\r\n
    \                           </mml:msup>\r\n                            <mml:mrow>\r\n
    \                             <mml:mo>(</mml:mo>\r\n                              <mml:mrow>\r\n
    \                               <mml:mo>[</mml:mo>\r\n                                <mml:mn>0</mml:mn>\r\n
    \                               <mml:mo>,</mml:mo>\r\n                                <mml:mi>∞</mml:mi>\r\n
    \                               <mml:mo>)</mml:mo>\r\n                              </mml:mrow>\r\n
    \                             <mml:mo>)</mml:mo>\r\n                            </mml:mrow>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   are such that\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$f(0)=0$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mi>f</mml:mi>\r\n
    \                           <mml:mo>(</mml:mo>\r\n                            <mml:mn>0</mml:mn>\r\n
    \                           <mml:mo>)</mml:mo>\r\n                            <mml:mo>=</mml:mo>\r\n
    \                           <mml:mn>0</mml:mn>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    and\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$|f(\\xi
    )| \\le K_f \\cdot (\\xi +1)^\\alpha $$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:mrow>\r\n                              <mml:mo>|</mml:mo>\r\n
    \                             <mml:mi>f</mml:mi>\r\n                              <mml:mrow>\r\n
    \                               <mml:mo>(</mml:mo>\r\n                                <mml:mi>ξ</mml:mi>\r\n
    \                               <mml:mo>)</mml:mo>\r\n                              </mml:mrow>\r\n
    \                             <mml:mo>|</mml:mo>\r\n                            </mml:mrow>\r\n
    \                           <mml:mo>≤</mml:mo>\r\n                            <mml:msub>\r\n
    \                             <mml:mi>K</mml:mi>\r\n                              <mml:mi>f</mml:mi>\r\n
    \                           </mml:msub>\r\n                            <mml:mo>·</mml:mo>\r\n
    \                           <mml:msup>\r\n                              <mml:mrow>\r\n
    \                               <mml:mo>(</mml:mo>\r\n                                <mml:mi>ξ</mml:mi>\r\n
    \                               <mml:mo>+</mml:mo>\r\n                                <mml:mn>1</mml:mn>\r\n
    \                               <mml:mo>)</mml:mo>\r\n                              </mml:mrow>\r\n
    \                             <mml:mi>α</mml:mi>\r\n                            </mml:msup>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   for all\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$\\xi \\ge 0$$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:mi>ξ</mml:mi>\r\n                            <mml:mo>≥</mml:mo>\r\n
    \                           <mml:mn>0</mml:mn>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    and some\r\n
    \                   <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$K_f&gt;0$$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:msub>\r\n                              <mml:mi>K</mml:mi>\r\n
    \                             <mml:mi>f</mml:mi>\r\n                            </mml:msub>\r\n
    \                           <mml:mo>&gt;</mml:mo>\r\n                            <mml:mn>0</mml:mn>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   and\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$\\alpha &lt;\\frac{3}{2}$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mi>α</mml:mi>\r\n
    \                           <mml:mo>&lt;</mml:mo>\r\n                            <mml:mfrac>\r\n
    \                             <mml:mn>3</mml:mn>\r\n                              <mml:mn>2</mml:mn>\r\n
    \                           </mml:mfrac>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    , and that\r\n
    \                   <jats:disp-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$\\begin{aligned} \\gamma _0 \\le \\gamma
    (\\xi ) \\le \\gamma _0 + \\delta \\qquad \\hbox {for all } \\xi \\ge 0. \\end{aligned}$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mtable>\r\n
    \                             <mml:mtr>\r\n                                <mml:mtd>\r\n
    \                                 <mml:mrow>\r\n                                    <mml:msub>\r\n
    \                                     <mml:mi>γ</mml:mi>\r\n                                      <mml:mn>0</mml:mn>\r\n
    \                                   </mml:msub>\r\n                                    <mml:mo>≤</mml:mo>\r\n
    \                                   <mml:mi>γ</mml:mi>\r\n                                    <mml:mrow>\r\n
    \                                     <mml:mo>(</mml:mo>\r\n                                      <mml:mi>ξ</mml:mi>\r\n
    \                                     <mml:mo>)</mml:mo>\r\n                                    </mml:mrow>\r\n
    \                                   <mml:mo>≤</mml:mo>\r\n                                    <mml:msub>\r\n
    \                                     <mml:mi>γ</mml:mi>\r\n                                      <mml:mn>0</mml:mn>\r\n
    \                                   </mml:msub>\r\n                                    <mml:mo>+</mml:mo>\r\n
    \                                   <mml:mi>δ</mml:mi>\r\n                                    <mml:mspace/>\r\n
    \                                   <mml:mtext>for all</mml:mtext>\r\n                                    <mml:mspace/>\r\n
    \                                   <mml:mi>ξ</mml:mi>\r\n                                    <mml:mo>≥</mml:mo>\r\n
    \                                   <mml:mn>0</mml:mn>\r\n                                    <mml:mo>.</mml:mo>\r\n
    \                                 </mml:mrow>\r\n                                </mml:mtd>\r\n
    \                             </mml:mtr>\r\n                            </mml:mtable>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:disp-formula>\r\n
    \                   This is supplemented by a statement on global existence of
    certain strong solutions, particularly continuous in both components, under weaker
    conditions on the initial data.\r\n                  </jats:p>"
article_number: '108'
author:
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Winkler M. Large-data regular solutions in a one-dimensional thermoviscoelastic
    evolution problem involving temperature-dependent viscosities. <i>Journal of Evolution
    Equations</i>. 2025;25(4). doi:<a href="https://doi.org/10.1007/s00028-025-01144-z">10.1007/s00028-025-01144-z</a>
  apa: Winkler, M. (2025). Large-data regular solutions in a one-dimensional thermoviscoelastic
    evolution problem involving temperature-dependent viscosities. <i>Journal of Evolution
    Equations</i>, <i>25</i>(4), Article 108. <a href="https://doi.org/10.1007/s00028-025-01144-z">https://doi.org/10.1007/s00028-025-01144-z</a>
  bibtex: '@article{Winkler_2025, title={Large-data regular solutions in a one-dimensional
    thermoviscoelastic evolution problem involving temperature-dependent viscosities},
    volume={25}, DOI={<a href="https://doi.org/10.1007/s00028-025-01144-z">10.1007/s00028-025-01144-z</a>},
    number={4108}, journal={Journal of Evolution Equations}, publisher={Springer Science
    and Business Media LLC}, author={Winkler, Michael}, year={2025} }'
  chicago: Winkler, Michael. “Large-Data Regular Solutions in a One-Dimensional Thermoviscoelastic
    Evolution Problem Involving Temperature-Dependent Viscosities.” <i>Journal of
    Evolution Equations</i> 25, no. 4 (2025). <a href="https://doi.org/10.1007/s00028-025-01144-z">https://doi.org/10.1007/s00028-025-01144-z</a>.
  ieee: 'M. Winkler, “Large-data regular solutions in a one-dimensional thermoviscoelastic
    evolution problem involving temperature-dependent viscosities,” <i>Journal of
    Evolution Equations</i>, vol. 25, no. 4, Art. no. 108, 2025, doi: <a href="https://doi.org/10.1007/s00028-025-01144-z">10.1007/s00028-025-01144-z</a>.'
  mla: Winkler, Michael. “Large-Data Regular Solutions in a One-Dimensional Thermoviscoelastic
    Evolution Problem Involving Temperature-Dependent Viscosities.” <i>Journal of
    Evolution Equations</i>, vol. 25, no. 4, 108, Springer Science and Business Media
    LLC, 2025, doi:<a href="https://doi.org/10.1007/s00028-025-01144-z">10.1007/s00028-025-01144-z</a>.
  short: M. Winkler, Journal of Evolution Equations 25 (2025).
date_created: 2025-12-18T19:02:51Z
date_updated: 2025-12-18T20:13:11Z
doi: 10.1007/s00028-025-01144-z
intvolume: '        25'
issue: '4'
language:
- iso: eng
publication: Journal of Evolution Equations
publication_identifier:
  issn:
  - 1424-3199
  - 1424-3202
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Large-data regular solutions in a one-dimensional thermoviscoelastic evolution
  problem involving temperature-dependent viscosities
type: journal_article
user_id: '31496'
volume: 25
year: '2025'
...
---
_id: '63246'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n                  <jats:p>\r\n                    The
    hyperbolic-parabolic model\r\n                    <jats:disp-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$\\begin{aligned} \\left\\{ \\begin{array}{ll}
    u_{tt} = u_{xx} - \\big (f(\\Theta )\\big )_x, \\qquad &amp;  x\\in \\Omega ,
    \\ t&gt;0, \\\\ \\Theta _t = \\Theta _{xx} - f(\\Theta ) u_{xt}, \\qquad &amp;
    \ x\\in \\Omega , \\ t&gt;0, \\end{array} \\right. \\end{aligned}$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mtable>\r\n
    \                             <mml:mtr>\r\n                                <mml:mtd>\r\n
    \                                 <mml:mfenced>\r\n                                    <mml:mrow>\r\n
    \                                     <mml:mtable>\r\n                                        <mml:mtr>\r\n
    \                                         <mml:mtd>\r\n                                            <mml:mrow>\r\n
    \                                             <mml:msub>\r\n                                                <mml:mi>u</mml:mi>\r\n
    \                                               <mml:mrow>\r\n                                                  <mml:mi>tt</mml:mi>\r\n
    \                                               </mml:mrow>\r\n                                              </mml:msub>\r\n
    \                                             <mml:mo>=</mml:mo>\r\n                                              <mml:msub>\r\n
    \                                               <mml:mi>u</mml:mi>\r\n                                                <mml:mrow>\r\n
    \                                                 <mml:mi>xx</mml:mi>\r\n                                                </mml:mrow>\r\n
    \                                             </mml:msub>\r\n                                              <mml:mo>-</mml:mo>\r\n
    \                                             <mml:mrow>\r\n                                                <mml:mo>(</mml:mo>\r\n
    \                                             </mml:mrow>\r\n                                              <mml:mi>f</mml:mi>\r\n
    \                                             <mml:mrow>\r\n                                                <mml:mo>(</mml:mo>\r\n
    \                                               <mml:mi>Θ</mml:mi>\r\n                                                <mml:mo>)</mml:mo>\r\n
    \                                             </mml:mrow>\r\n                                              <mml:msub>\r\n
    \                                               <mml:mrow>\r\n                                                  <mml:mo>)</mml:mo>\r\n
    \                                               </mml:mrow>\r\n                                                <mml:mi>x</mml:mi>\r\n
    \                                             </mml:msub>\r\n                                              <mml:mo>,</mml:mo>\r\n
    \                                             <mml:mspace/>\r\n                                            </mml:mrow>\r\n
    \                                         </mml:mtd>\r\n                                          <mml:mtd>\r\n
    \                                           <mml:mrow>\r\n                                              <mml:mi>x</mml:mi>\r\n
    \                                             <mml:mo>∈</mml:mo>\r\n                                              <mml:mi>Ω</mml:mi>\r\n
    \                                             <mml:mo>,</mml:mo>\r\n                                              <mml:mspace/>\r\n
    \                                             <mml:mi>t</mml:mi>\r\n                                              <mml:mo>&gt;</mml:mo>\r\n
    \                                             <mml:mn>0</mml:mn>\r\n                                              <mml:mo>,</mml:mo>\r\n
    \                                           </mml:mrow>\r\n                                          </mml:mtd>\r\n
    \                                       </mml:mtr>\r\n                                        <mml:mtr>\r\n
    \                                         <mml:mtd>\r\n                                            <mml:mrow>\r\n
    \                                             <mml:mrow/>\r\n                                              <mml:msub>\r\n
    \                                               <mml:mi>Θ</mml:mi>\r\n                                                <mml:mi>t</mml:mi>\r\n
    \                                             </mml:msub>\r\n                                              <mml:mo>=</mml:mo>\r\n
    \                                             <mml:msub>\r\n                                                <mml:mi>Θ</mml:mi>\r\n
    \                                               <mml:mrow>\r\n                                                  <mml:mi>xx</mml:mi>\r\n
    \                                               </mml:mrow>\r\n                                              </mml:msub>\r\n
    \                                             <mml:mo>-</mml:mo>\r\n                                              <mml:mi>f</mml:mi>\r\n
    \                                             <mml:mrow>\r\n                                                <mml:mo>(</mml:mo>\r\n
    \                                               <mml:mi>Θ</mml:mi>\r\n                                                <mml:mo>)</mml:mo>\r\n
    \                                             </mml:mrow>\r\n                                              <mml:msub>\r\n
    \                                               <mml:mi>u</mml:mi>\r\n                                                <mml:mrow>\r\n
    \                                                 <mml:mi>xt</mml:mi>\r\n                                                </mml:mrow>\r\n
    \                                             </mml:msub>\r\n                                              <mml:mo>,</mml:mo>\r\n
    \                                             <mml:mspace/>\r\n                                            </mml:mrow>\r\n
    \                                         </mml:mtd>\r\n                                          <mml:mtd>\r\n
    \                                           <mml:mrow>\r\n                                              <mml:mi>x</mml:mi>\r\n
    \                                             <mml:mo>∈</mml:mo>\r\n                                              <mml:mi>Ω</mml:mi>\r\n
    \                                             <mml:mo>,</mml:mo>\r\n                                              <mml:mspace/>\r\n
    \                                             <mml:mi>t</mml:mi>\r\n                                              <mml:mo>&gt;</mml:mo>\r\n
    \                                             <mml:mn>0</mml:mn>\r\n                                              <mml:mo>,</mml:mo>\r\n
    \                                           </mml:mrow>\r\n                                          </mml:mtd>\r\n
    \                                       </mml:mtr>\r\n                                      </mml:mtable>\r\n
    \                                   </mml:mrow>\r\n                                  </mml:mfenced>\r\n
    \                               </mml:mtd>\r\n                              </mml:mtr>\r\n
    \                           </mml:mtable>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:disp-formula>\r\n                    for the evolution
    of the displacement variable\r\n                    <jats:italic>u</jats:italic>\r\n
    \                   and the temperature\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$\\Theta
    \\ge 0$$</jats:tex-math>\r\n                        <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mi>Θ</mml:mi>\r\n
    \                           <mml:mo>≥</mml:mo>\r\n                            <mml:mn>0</mml:mn>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   during thermoelastic interaction in a one-dimensional bounded
    interval\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$\\Omega $$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mi>Ω</mml:mi>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    is considered.
    Whereas the literature has provided comprehensive results on global solutions
    for sufficiently regular initial data\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$(u_0,u_{0t},\\Theta
    _0)=(u,u_t,\\Theta )|_{t=0}$$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:mrow>\r\n                              <mml:mo>(</mml:mo>\r\n
    \                             <mml:msub>\r\n                                <mml:mi>u</mml:mi>\r\n
    \                               <mml:mn>0</mml:mn>\r\n                              </mml:msub>\r\n
    \                             <mml:mo>,</mml:mo>\r\n                              <mml:msub>\r\n
    \                               <mml:mi>u</mml:mi>\r\n                                <mml:mrow>\r\n
    \                                 <mml:mn>0</mml:mn>\r\n                                  <mml:mi>t</mml:mi>\r\n
    \                               </mml:mrow>\r\n                              </mml:msub>\r\n
    \                             <mml:mo>,</mml:mo>\r\n                              <mml:msub>\r\n
    \                               <mml:mi>Θ</mml:mi>\r\n                                <mml:mn>0</mml:mn>\r\n
    \                             </mml:msub>\r\n                              <mml:mo>)</mml:mo>\r\n
    \                           </mml:mrow>\r\n                            <mml:mo>=</mml:mo>\r\n
    \                           <mml:mrow>\r\n                              <mml:mo>(</mml:mo>\r\n
    \                             <mml:mi>u</mml:mi>\r\n                              <mml:mo>,</mml:mo>\r\n
    \                             <mml:msub>\r\n                                <mml:mi>u</mml:mi>\r\n
    \                               <mml:mi>t</mml:mi>\r\n                              </mml:msub>\r\n
    \                             <mml:mo>,</mml:mo>\r\n                              <mml:mi>Θ</mml:mi>\r\n
    \                             <mml:mo>)</mml:mo>\r\n                            </mml:mrow>\r\n
    \                           <mml:msub>\r\n                              <mml:mrow>\r\n
    \                               <mml:mo>|</mml:mo>\r\n                              </mml:mrow>\r\n
    \                             <mml:mrow>\r\n                                <mml:mi>t</mml:mi>\r\n
    \                               <mml:mo>=</mml:mo>\r\n                                <mml:mn>0</mml:mn>\r\n
    \                             </mml:mrow>\r\n                            </mml:msub>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   when\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$f\\equiv id$$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:mi>f</mml:mi>\r\n                            <mml:mo>≡</mml:mo>\r\n
    \                           <mml:mi>i</mml:mi>\r\n                            <mml:mi>d</mml:mi>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   , it seems to have remained open so far how far a solution
    theory can be built solely on the two fundamental physical principles of energy
    conservation and entropy nondecrease. The present manuscript addresses this by
    asserting global existence of weak solutions under assumptions which are energy-
    and entropy-minimal in the sense of allowing for any initial data\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$u_0\\in
    W_0^{1,2}(\\Omega )$$</jats:tex-math>\r\n                        <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:msub>\r\n
    \                             <mml:mi>u</mml:mi>\r\n                              <mml:mn>0</mml:mn>\r\n
    \                           </mml:msub>\r\n                            <mml:mo>∈</mml:mo>\r\n
    \                           <mml:msubsup>\r\n                              <mml:mi>W</mml:mi>\r\n
    \                             <mml:mn>0</mml:mn>\r\n                              <mml:mrow>\r\n
    \                               <mml:mn>1</mml:mn>\r\n                                <mml:mo>,</mml:mo>\r\n
    \                               <mml:mn>2</mml:mn>\r\n                              </mml:mrow>\r\n
    \                           </mml:msubsup>\r\n                            <mml:mrow>\r\n
    \                             <mml:mo>(</mml:mo>\r\n                              <mml:mi>Ω</mml:mi>\r\n
    \                             <mml:mo>)</mml:mo>\r\n                            </mml:mrow>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   ,\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$u_{0t} \\in L^2(\\Omega )$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:msub>\r\n
    \                             <mml:mi>u</mml:mi>\r\n                              <mml:mrow>\r\n
    \                               <mml:mn>0</mml:mn>\r\n                                <mml:mi>t</mml:mi>\r\n
    \                             </mml:mrow>\r\n                            </mml:msub>\r\n
    \                           <mml:mo>∈</mml:mo>\r\n                            <mml:msup>\r\n
    \                             <mml:mi>L</mml:mi>\r\n                              <mml:mn>2</mml:mn>\r\n
    \                           </mml:msup>\r\n                            <mml:mrow>\r\n
    \                             <mml:mo>(</mml:mo>\r\n                              <mml:mi>Ω</mml:mi>\r\n
    \                             <mml:mo>)</mml:mo>\r\n                            </mml:mrow>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   and\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$0\\le \\Theta _0\\in L^1(\\Omega )$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mn>0</mml:mn>\r\n
    \                           <mml:mo>≤</mml:mo>\r\n                            <mml:msub>\r\n
    \                             <mml:mi>Θ</mml:mi>\r\n                              <mml:mn>0</mml:mn>\r\n
    \                           </mml:msub>\r\n                            <mml:mo>∈</mml:mo>\r\n
    \                           <mml:msup>\r\n                              <mml:mi>L</mml:mi>\r\n
    \                             <mml:mn>1</mml:mn>\r\n                            </mml:msup>\r\n
    \                           <mml:mrow>\r\n                              <mml:mo>(</mml:mo>\r\n
    \                             <mml:mi>Ω</mml:mi>\r\n                              <mml:mo>)</mml:mo>\r\n
    \                           </mml:mrow>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    , and which
    apply to arbitrary\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$f\\in C^1([0,\\infty ))$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mi>f</mml:mi>\r\n
    \                           <mml:mo>∈</mml:mo>\r\n                            <mml:msup>\r\n
    \                             <mml:mi>C</mml:mi>\r\n                              <mml:mn>1</mml:mn>\r\n
    \                           </mml:msup>\r\n                            <mml:mrow>\r\n
    \                             <mml:mo>(</mml:mo>\r\n                              <mml:mrow>\r\n
    \                               <mml:mo>[</mml:mo>\r\n                                <mml:mn>0</mml:mn>\r\n
    \                               <mml:mo>,</mml:mo>\r\n                                <mml:mi>∞</mml:mi>\r\n
    \                               <mml:mo>)</mml:mo>\r\n                              </mml:mrow>\r\n
    \                             <mml:mo>)</mml:mo>\r\n                            </mml:mrow>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   with\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$f(0)=0$$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:mi>f</mml:mi>\r\n                            <mml:mo>(</mml:mo>\r\n
    \                           <mml:mn>0</mml:mn>\r\n                            <mml:mo>)</mml:mo>\r\n
    \                           <mml:mo>=</mml:mo>\r\n                            <mml:mn>0</mml:mn>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   and\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$f'&gt;0$$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:msup>\r\n                              <mml:mi>f</mml:mi>\r\n
    \                             <mml:mo>′</mml:mo>\r\n                            </mml:msup>\r\n
    \                           <mml:mo>&gt;</mml:mo>\r\n                            <mml:mn>0</mml:mn>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   on\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$[0,\\infty )$$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:mo>[</mml:mo>\r\n                            <mml:mn>0</mml:mn>\r\n
    \                           <mml:mo>,</mml:mo>\r\n                            <mml:mi>∞</mml:mi>\r\n
    \                           <mml:mo>)</mml:mo>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    .\r\n                  </jats:p>"
article_number: '1'
author:
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Winkler M. Rough solutions in one-dimensional nonlinear thermoelasticity. <i>Calculus
    of Variations and Partial Differential Equations</i>. 2025;65(1). doi:<a href="https://doi.org/10.1007/s00526-025-03170-8">10.1007/s00526-025-03170-8</a>
  apa: Winkler, M. (2025). Rough solutions in one-dimensional nonlinear thermoelasticity.
    <i>Calculus of Variations and Partial Differential Equations</i>, <i>65</i>(1),
    Article 1. <a href="https://doi.org/10.1007/s00526-025-03170-8">https://doi.org/10.1007/s00526-025-03170-8</a>
  bibtex: '@article{Winkler_2025, title={Rough solutions in one-dimensional nonlinear
    thermoelasticity}, volume={65}, DOI={<a href="https://doi.org/10.1007/s00526-025-03170-8">10.1007/s00526-025-03170-8</a>},
    number={11}, journal={Calculus of Variations and Partial Differential Equations},
    publisher={Springer Science and Business Media LLC}, author={Winkler, Michael},
    year={2025} }'
  chicago: Winkler, Michael. “Rough Solutions in One-Dimensional Nonlinear Thermoelasticity.”
    <i>Calculus of Variations and Partial Differential Equations</i> 65, no. 1 (2025).
    <a href="https://doi.org/10.1007/s00526-025-03170-8">https://doi.org/10.1007/s00526-025-03170-8</a>.
  ieee: 'M. Winkler, “Rough solutions in one-dimensional nonlinear thermoelasticity,”
    <i>Calculus of Variations and Partial Differential Equations</i>, vol. 65, no.
    1, Art. no. 1, 2025, doi: <a href="https://doi.org/10.1007/s00526-025-03170-8">10.1007/s00526-025-03170-8</a>.'
  mla: Winkler, Michael. “Rough Solutions in One-Dimensional Nonlinear Thermoelasticity.”
    <i>Calculus of Variations and Partial Differential Equations</i>, vol. 65, no.
    1, 1, Springer Science and Business Media LLC, 2025, doi:<a href="https://doi.org/10.1007/s00526-025-03170-8">10.1007/s00526-025-03170-8</a>.
  short: M. Winkler, Calculus of Variations and Partial Differential Equations 65
    (2025).
date_created: 2025-12-18T19:01:02Z
date_updated: 2025-12-18T20:12:50Z
doi: 10.1007/s00526-025-03170-8
intvolume: '        65'
issue: '1'
language:
- iso: eng
publication: Calculus of Variations and Partial Differential Equations
publication_identifier:
  issn:
  - 0944-2669
  - 1432-0835
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Rough solutions in one-dimensional nonlinear thermoelasticity
type: journal_article
user_id: '31496'
volume: 65
year: '2025'
...
---
_id: '63244'
abstract:
- lang: eng
  text: "<jats:p>\r\n            The Cauchy problem in \r\n            <jats:inline-formula>\r\n
    \             <jats:tex-math>\\mathbb{R}^{n}</jats:tex-math>\r\n            </jats:inline-formula>\r\n
    \            for the cross-diffusion system \r\n          </jats:p>\r\n          <jats:p>\r\n
    \           <jats:disp-formula>\r\n              <jats:tex-math>\\begin{cases}u_{t}
    = \\nabla \\cdot (D(u)\\nabla u) - \\nabla\\cdot (u\\nabla v), \\\\ 0 = \\Delta
    v +u,\\end{cases}</jats:tex-math>\r\n            </jats:disp-formula>\r\n          </jats:p>\r\n
    \         <jats:p>\r\n             is considered for \r\n            <jats:inline-formula>\r\n
    \             <jats:tex-math>n\\ge 2</jats:tex-math>\r\n            </jats:inline-formula>\r\n
    \            and under assumptions ensuring that \r\n            <jats:inline-formula>\r\n
    \             <jats:tex-math>D</jats:tex-math>\r\n            </jats:inline-formula>\r\n
    \            suitably generalizes the prototype given by \r\n          </jats:p>\r\n
    \         <jats:p>\r\n            <jats:disp-formula>\r\n              <jats:tex-math>D(\\xi)=(\\xi+1)^{-\\alpha},
    \\quad \\xi\\ge 0.</jats:tex-math>\r\n            </jats:disp-formula>\r\n          </jats:p>\r\n
    \         <jats:p>\r\n             Under the assumption that \r\n            <jats:inline-formula>\r\n
    \             <jats:tex-math>\\alpha&gt;1</jats:tex-math>\r\n            </jats:inline-formula>\r\n
    \           , it is shown that for any \r\n            <jats:inline-formula>\r\n
    \             <jats:tex-math>r_{\\star}&gt;0</jats:tex-math>\r\n            </jats:inline-formula>\r\n
    \            and \r\n            <jats:inline-formula>\r\n              <jats:tex-math>\\delta\\in
    (0,1)</jats:tex-math>\r\n            </jats:inline-formula>\r\n             one
    can find radially symmetric initial data from \r\n            <jats:inline-formula>\r\n
    \             <jats:tex-math>C_{0}^{\\infty}(\\mathbb{R}^{n})</jats:tex-math>\r\n
    \           </jats:inline-formula>\r\n             such that the corresponding
    solution blows up within some finite time, and that this explosion occurs throughout
    certain spheres in an appropriate sense, with any such sphere being located in
    the annulus \r\n            <jats:inline-formula>\r\n              <jats:tex-math>\\overline{B}_{r_\\star+\\delta}(0)\\setminus
    B_{(1-\\delta)r_\\star}(0)</jats:tex-math>\r\n            </jats:inline-formula>\r\n
    \           .This is complemented by a result revealing that when \r\n            <jats:inline-formula>\r\n
    \             <jats:tex-math>\\alpha&lt;1</jats:tex-math>\r\n            </jats:inline-formula>\r\n
    \           , any finite-mass unbounded radial solution must blow up exclusively
    at the spatial origin.\r\n          </jats:p>"
author:
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Winkler M. Can diffusion degeneracies enhance complexity in chemotactic aggregation?
    Finite-time blow-up on spheres in a quasilinear Keller–Segel system. <i>Journal
    of the European Mathematical Society</i>. Published online 2025. doi:<a href="https://doi.org/10.4171/jems/1607">10.4171/jems/1607</a>
  apa: Winkler, M. (2025). Can diffusion degeneracies enhance complexity in chemotactic
    aggregation? Finite-time blow-up on spheres in a quasilinear Keller–Segel system.
    <i>Journal of the European Mathematical Society</i>. <a href="https://doi.org/10.4171/jems/1607">https://doi.org/10.4171/jems/1607</a>
  bibtex: '@article{Winkler_2025, title={Can diffusion degeneracies enhance complexity
    in chemotactic aggregation? Finite-time blow-up on spheres in a quasilinear Keller–Segel
    system}, DOI={<a href="https://doi.org/10.4171/jems/1607">10.4171/jems/1607</a>},
    journal={Journal of the European Mathematical Society}, publisher={European Mathematical
    Society - EMS - Publishing House GmbH}, author={Winkler, Michael}, year={2025}
    }'
  chicago: Winkler, Michael. “Can Diffusion Degeneracies Enhance Complexity in Chemotactic
    Aggregation? Finite-Time Blow-up on Spheres in a Quasilinear Keller–Segel System.”
    <i>Journal of the European Mathematical Society</i>, 2025. <a href="https://doi.org/10.4171/jems/1607">https://doi.org/10.4171/jems/1607</a>.
  ieee: 'M. Winkler, “Can diffusion degeneracies enhance complexity in chemotactic
    aggregation? Finite-time blow-up on spheres in a quasilinear Keller–Segel system,”
    <i>Journal of the European Mathematical Society</i>, 2025, doi: <a href="https://doi.org/10.4171/jems/1607">10.4171/jems/1607</a>.'
  mla: Winkler, Michael. “Can Diffusion Degeneracies Enhance Complexity in Chemotactic
    Aggregation? Finite-Time Blow-up on Spheres in a Quasilinear Keller–Segel System.”
    <i>Journal of the European Mathematical Society</i>, European Mathematical Society
    - EMS - Publishing House GmbH, 2025, doi:<a href="https://doi.org/10.4171/jems/1607">10.4171/jems/1607</a>.
  short: M. Winkler, Journal of the European Mathematical Society (2025).
date_created: 2025-12-18T18:59:39Z
date_updated: 2025-12-18T20:12:36Z
doi: 10.4171/jems/1607
language:
- iso: eng
publication: Journal of the European Mathematical Society
publication_identifier:
  issn:
  - 1435-9855
  - 1435-9863
publication_status: published
publisher: European Mathematical Society - EMS - Publishing House GmbH
status: public
title: Can diffusion degeneracies enhance complexity in chemotactic aggregation? Finite-time
  blow-up on spheres in a quasilinear Keller–Segel system
type: journal_article
user_id: '31496'
year: '2025'
...
---
_id: '63247'
author:
- first_name: Youshan
  full_name: Tao, Youshan
  last_name: Tao
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Tao Y, Winkler M. A switch in dimension dependence of critical blow-up exponents
    in a Keller-Segel system involving indirect signal production. <i>Journal of Differential
    Equations</i>. 2025;423:197-239. doi:<a href="https://doi.org/10.1016/j.jde.2024.12.040">10.1016/j.jde.2024.12.040</a>
  apa: Tao, Y., &#38; Winkler, M. (2025). A switch in dimension dependence of critical
    blow-up exponents in a Keller-Segel system involving indirect signal production.
    <i>Journal of Differential Equations</i>, <i>423</i>, 197–239. <a href="https://doi.org/10.1016/j.jde.2024.12.040">https://doi.org/10.1016/j.jde.2024.12.040</a>
  bibtex: '@article{Tao_Winkler_2025, title={A switch in dimension dependence of critical
    blow-up exponents in a Keller-Segel system involving indirect signal production},
    volume={423}, DOI={<a href="https://doi.org/10.1016/j.jde.2024.12.040">10.1016/j.jde.2024.12.040</a>},
    journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Tao,
    Youshan and Winkler, Michael}, year={2025}, pages={197–239} }'
  chicago: 'Tao, Youshan, and Michael Winkler. “A Switch in Dimension Dependence of
    Critical Blow-up Exponents in a Keller-Segel System Involving Indirect Signal
    Production.” <i>Journal of Differential Equations</i> 423 (2025): 197–239. <a
    href="https://doi.org/10.1016/j.jde.2024.12.040">https://doi.org/10.1016/j.jde.2024.12.040</a>.'
  ieee: 'Y. Tao and M. Winkler, “A switch in dimension dependence of critical blow-up
    exponents in a Keller-Segel system involving indirect signal production,” <i>Journal
    of Differential Equations</i>, vol. 423, pp. 197–239, 2025, doi: <a href="https://doi.org/10.1016/j.jde.2024.12.040">10.1016/j.jde.2024.12.040</a>.'
  mla: Tao, Youshan, and Michael Winkler. “A Switch in Dimension Dependence of Critical
    Blow-up Exponents in a Keller-Segel System Involving Indirect Signal Production.”
    <i>Journal of Differential Equations</i>, vol. 423, Elsevier BV, 2025, pp. 197–239,
    doi:<a href="https://doi.org/10.1016/j.jde.2024.12.040">10.1016/j.jde.2024.12.040</a>.
  short: Y. Tao, M. Winkler, Journal of Differential Equations 423 (2025) 197–239.
date_created: 2025-12-18T19:01:40Z
date_updated: 2025-12-18T20:12:58Z
doi: 10.1016/j.jde.2024.12.040
intvolume: '       423'
language:
- iso: eng
page: 197-239
publication: Journal of Differential Equations
publication_identifier:
  issn:
  - 0022-0396
publication_status: published
publisher: Elsevier BV
status: public
title: A switch in dimension dependence of critical blow-up exponents in a Keller-Segel
  system involving indirect signal production
type: journal_article
user_id: '31496'
volume: 423
year: '2025'
...
---
_id: '63252'
author:
- first_name: Youshan
  full_name: Tao, Youshan
  last_name: Tao
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Tao Y, Winkler M. A unified approach to existence theories for singular chemotaxis
    systems with nonlinear signal production. <i>Science China Mathematics</i>. 2025;68(12):2867-2900.
    doi:<a href="https://doi.org/10.1007/s11425-023-2397-y">10.1007/s11425-023-2397-y</a>
  apa: Tao, Y., &#38; Winkler, M. (2025). A unified approach to existence theories
    for singular chemotaxis systems with nonlinear signal production. <i>Science China
    Mathematics</i>, <i>68</i>(12), 2867–2900. <a href="https://doi.org/10.1007/s11425-023-2397-y">https://doi.org/10.1007/s11425-023-2397-y</a>
  bibtex: '@article{Tao_Winkler_2025, title={A unified approach to existence theories
    for singular chemotaxis systems with nonlinear signal production}, volume={68},
    DOI={<a href="https://doi.org/10.1007/s11425-023-2397-y">10.1007/s11425-023-2397-y</a>},
    number={12}, journal={Science China Mathematics}, publisher={Springer Science
    and Business Media LLC}, author={Tao, Youshan and Winkler, Michael}, year={2025},
    pages={2867–2900} }'
  chicago: 'Tao, Youshan, and Michael Winkler. “A Unified Approach to Existence Theories
    for Singular Chemotaxis Systems with Nonlinear Signal Production.” <i>Science
    China Mathematics</i> 68, no. 12 (2025): 2867–2900. <a href="https://doi.org/10.1007/s11425-023-2397-y">https://doi.org/10.1007/s11425-023-2397-y</a>.'
  ieee: 'Y. Tao and M. Winkler, “A unified approach to existence theories for singular
    chemotaxis systems with nonlinear signal production,” <i>Science China Mathematics</i>,
    vol. 68, no. 12, pp. 2867–2900, 2025, doi: <a href="https://doi.org/10.1007/s11425-023-2397-y">10.1007/s11425-023-2397-y</a>.'
  mla: Tao, Youshan, and Michael Winkler. “A Unified Approach to Existence Theories
    for Singular Chemotaxis Systems with Nonlinear Signal Production.” <i>Science
    China Mathematics</i>, vol. 68, no. 12, Springer Science and Business Media LLC,
    2025, pp. 2867–900, doi:<a href="https://doi.org/10.1007/s11425-023-2397-y">10.1007/s11425-023-2397-y</a>.
  short: Y. Tao, M. Winkler, Science China Mathematics 68 (2025) 2867–2900.
date_created: 2025-12-18T19:04:17Z
date_updated: 2025-12-18T20:13:40Z
doi: 10.1007/s11425-023-2397-y
intvolume: '        68'
issue: '12'
language:
- iso: eng
page: 2867-2900
publication: Science China Mathematics
publication_identifier:
  issn:
  - 1674-7283
  - 1869-1862
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: A unified approach to existence theories for singular chemotaxis systems with
  nonlinear signal production
type: journal_article
user_id: '31496'
volume: 68
year: '2025'
...
---
_id: '63344'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n          <jats:p>A Neumann-type initial-boundary
    value problem for <jats:disp-formula>\r\n              <jats:alternatives>\r\n
    \               <jats:tex-math>$$\\begin{aligned} \\left\\{ \\begin{array}{l}
    u_{tt} = \\nabla \\cdot (\\gamma (\\Theta ) \\nabla u_t) + a \\nabla \\cdot (\\gamma
    (\\Theta ) \\nabla u) + \\nabla \\cdot f(\\Theta ), \\\\ \\Theta _t = D\\Delta
    \\Theta + \\Gamma (\\Theta ) |\\nabla u_t|^2 + F(\\Theta )\\cdot \\nabla u_t,
    \\end{array} \\right. \\end{aligned}$$</jats:tex-math>\r\n                <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n
    \                   <mml:mtable>\r\n                      <mml:mtr>\r\n                        <mml:mtd>\r\n
    \                         <mml:mfenced>\r\n                            <mml:mrow>\r\n
    \                             <mml:mtable>\r\n                                <mml:mtr>\r\n
    \                                 <mml:mtd>\r\n                                    <mml:mrow>\r\n
    \                                     <mml:msub>\r\n                                        <mml:mi>u</mml:mi>\r\n
    \                                       <mml:mrow>\r\n                                          <mml:mi>tt</mml:mi>\r\n
    \                                       </mml:mrow>\r\n                                      </mml:msub>\r\n
    \                                     <mml:mo>=</mml:mo>\r\n                                      <mml:mi>∇</mml:mi>\r\n
    \                                     <mml:mo>·</mml:mo>\r\n                                      <mml:mrow>\r\n
    \                                       <mml:mo>(</mml:mo>\r\n                                        <mml:mi>γ</mml:mi>\r\n
    \                                       <mml:mrow>\r\n                                          <mml:mo>(</mml:mo>\r\n
    \                                         <mml:mi>Θ</mml:mi>\r\n                                          <mml:mo>)</mml:mo>\r\n
    \                                       </mml:mrow>\r\n                                        <mml:mi>∇</mml:mi>\r\n
    \                                       <mml:msub>\r\n                                          <mml:mi>u</mml:mi>\r\n
    \                                         <mml:mi>t</mml:mi>\r\n                                        </mml:msub>\r\n
    \                                       <mml:mo>)</mml:mo>\r\n                                      </mml:mrow>\r\n
    \                                     <mml:mo>+</mml:mo>\r\n                                      <mml:mi>a</mml:mi>\r\n
    \                                     <mml:mi>∇</mml:mi>\r\n                                      <mml:mo>·</mml:mo>\r\n
    \                                     <mml:mrow>\r\n                                        <mml:mo>(</mml:mo>\r\n
    \                                       <mml:mi>γ</mml:mi>\r\n                                        <mml:mrow>\r\n
    \                                         <mml:mo>(</mml:mo>\r\n                                          <mml:mi>Θ</mml:mi>\r\n
    \                                         <mml:mo>)</mml:mo>\r\n                                        </mml:mrow>\r\n
    \                                       <mml:mi>∇</mml:mi>\r\n                                        <mml:mi>u</mml:mi>\r\n
    \                                       <mml:mo>)</mml:mo>\r\n                                      </mml:mrow>\r\n
    \                                     <mml:mo>+</mml:mo>\r\n                                      <mml:mi>∇</mml:mi>\r\n
    \                                     <mml:mo>·</mml:mo>\r\n                                      <mml:mi>f</mml:mi>\r\n
    \                                     <mml:mrow>\r\n                                        <mml:mo>(</mml:mo>\r\n
    \                                       <mml:mi>Θ</mml:mi>\r\n                                        <mml:mo>)</mml:mo>\r\n
    \                                     </mml:mrow>\r\n                                      <mml:mo>,</mml:mo>\r\n
    \                                   </mml:mrow>\r\n                                  </mml:mtd>\r\n
    \                               </mml:mtr>\r\n                                <mml:mtr>\r\n
    \                                 <mml:mtd>\r\n                                    <mml:mrow>\r\n
    \                                     <mml:mrow/>\r\n                                      <mml:msub>\r\n
    \                                       <mml:mi>Θ</mml:mi>\r\n                                        <mml:mi>t</mml:mi>\r\n
    \                                     </mml:msub>\r\n                                      <mml:mo>=</mml:mo>\r\n
    \                                     <mml:mi>D</mml:mi>\r\n                                      <mml:mi>Δ</mml:mi>\r\n
    \                                     <mml:mi>Θ</mml:mi>\r\n                                      <mml:mo>+</mml:mo>\r\n
    \                                     <mml:mi>Γ</mml:mi>\r\n                                      <mml:mrow>\r\n
    \                                       <mml:mo>(</mml:mo>\r\n                                        <mml:mi>Θ</mml:mi>\r\n
    \                                       <mml:mo>)</mml:mo>\r\n                                      </mml:mrow>\r\n
    \                                     <mml:msup>\r\n                                        <mml:mrow>\r\n
    \                                         <mml:mo>|</mml:mo>\r\n                                          <mml:mi>∇</mml:mi>\r\n
    \                                         <mml:msub>\r\n                                            <mml:mi>u</mml:mi>\r\n
    \                                           <mml:mi>t</mml:mi>\r\n                                          </mml:msub>\r\n
    \                                         <mml:mo>|</mml:mo>\r\n                                        </mml:mrow>\r\n
    \                                       <mml:mn>2</mml:mn>\r\n                                      </mml:msup>\r\n
    \                                     <mml:mo>+</mml:mo>\r\n                                      <mml:mi>F</mml:mi>\r\n
    \                                     <mml:mrow>\r\n                                        <mml:mo>(</mml:mo>\r\n
    \                                       <mml:mi>Θ</mml:mi>\r\n                                        <mml:mo>)</mml:mo>\r\n
    \                                     </mml:mrow>\r\n                                      <mml:mo>·</mml:mo>\r\n
    \                                     <mml:mi>∇</mml:mi>\r\n                                      <mml:msub>\r\n
    \                                       <mml:mi>u</mml:mi>\r\n                                        <mml:mi>t</mml:mi>\r\n
    \                                     </mml:msub>\r\n                                      <mml:mo>,</mml:mo>\r\n
    \                                   </mml:mrow>\r\n                                  </mml:mtd>\r\n
    \                               </mml:mtr>\r\n                              </mml:mtable>\r\n
    \                           </mml:mrow>\r\n                          </mml:mfenced>\r\n
    \                       </mml:mtd>\r\n                      </mml:mtr>\r\n                    </mml:mtable>\r\n
    \                 </mml:mrow>\r\n                </mml:math>\r\n              </jats:alternatives>\r\n
    \           </jats:disp-formula>is considered in a smoothly bounded domain <jats:inline-formula>\r\n
    \             <jats:alternatives>\r\n                <jats:tex-math>$$\\Omega
    \\subset \\mathbb {R}^n$$</jats:tex-math>\r\n                <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mrow>\r\n                    <mml:mi>Ω</mml:mi>\r\n                    <mml:mo>⊂</mml:mo>\r\n
    \                   <mml:msup>\r\n                      <mml:mrow>\r\n                        <mml:mi>R</mml:mi>\r\n
    \                     </mml:mrow>\r\n                      <mml:mi>n</mml:mi>\r\n
    \                   </mml:msup>\r\n                  </mml:mrow>\r\n                </mml:math>\r\n
    \             </jats:alternatives>\r\n            </jats:inline-formula>, <jats:inline-formula>\r\n
    \             <jats:alternatives>\r\n                <jats:tex-math>$$n\\ge 1$$</jats:tex-math>\r\n
    \               <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mrow>\r\n                    <mml:mi>n</mml:mi>\r\n                    <mml:mo>≥</mml:mo>\r\n
    \                   <mml:mn>1</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math>\r\n
    \             </jats:alternatives>\r\n            </jats:inline-formula>. In the
    case when <jats:inline-formula>\r\n              <jats:alternatives>\r\n                <jats:tex-math>$$n=1$$</jats:tex-math>\r\n
    \               <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mrow>\r\n                    <mml:mi>n</mml:mi>\r\n                    <mml:mo>=</mml:mo>\r\n
    \                   <mml:mn>1</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math>\r\n
    \             </jats:alternatives>\r\n            </jats:inline-formula>, <jats:inline-formula>\r\n
    \             <jats:alternatives>\r\n                <jats:tex-math>$$\\gamma
    \\equiv \\Gamma $$</jats:tex-math>\r\n                <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mrow>\r\n                    <mml:mi>γ</mml:mi>\r\n                    <mml:mo>≡</mml:mo>\r\n
    \                   <mml:mi>Γ</mml:mi>\r\n                  </mml:mrow>\r\n                </mml:math>\r\n
    \             </jats:alternatives>\r\n            </jats:inline-formula> and <jats:inline-formula>\r\n
    \             <jats:alternatives>\r\n                <jats:tex-math>$$f\\equiv
    F$$</jats:tex-math>\r\n                <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mrow>\r\n                    <mml:mi>f</mml:mi>\r\n                    <mml:mo>≡</mml:mo>\r\n
    \                   <mml:mi>F</mml:mi>\r\n                  </mml:mrow>\r\n                </mml:math>\r\n
    \             </jats:alternatives>\r\n            </jats:inline-formula>, this
    system coincides with the standard model for heat generation in a viscoelastic
    material of Kelvin-Voigt type, well-understood in situations in which <jats:inline-formula>\r\n
    \             <jats:alternatives>\r\n                <jats:tex-math>$$\\gamma
    =const$$</jats:tex-math>\r\n                <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mrow>\r\n                    <mml:mi>γ</mml:mi>\r\n                    <mml:mo>=</mml:mo>\r\n
    \                   <mml:mi>c</mml:mi>\r\n                    <mml:mi>o</mml:mi>\r\n
    \                   <mml:mi>n</mml:mi>\r\n                    <mml:mi>s</mml:mi>\r\n
    \                   <mml:mi>t</mml:mi>\r\n                  </mml:mrow>\r\n                </mml:math>\r\n
    \             </jats:alternatives>\r\n            </jats:inline-formula>. Covering
    scenarios in which all key ingredients <jats:inline-formula>\r\n              <jats:alternatives>\r\n
    \               <jats:tex-math>$$\\gamma ,\\Gamma ,f$$</jats:tex-math>\r\n                <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n
    \                   <mml:mi>γ</mml:mi>\r\n                    <mml:mo>,</mml:mo>\r\n
    \                   <mml:mi>Γ</mml:mi>\r\n                    <mml:mo>,</mml:mo>\r\n
    \                   <mml:mi>f</mml:mi>\r\n                  </mml:mrow>\r\n                </mml:math>\r\n
    \             </jats:alternatives>\r\n            </jats:inline-formula> and <jats:italic>F</jats:italic>
    may depend on the temperature <jats:inline-formula>\r\n              <jats:alternatives>\r\n
    \               <jats:tex-math>$$\\Theta $$</jats:tex-math>\r\n                <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mi>Θ</mml:mi>\r\n
    \               </mml:math>\r\n              </jats:alternatives>\r\n            </jats:inline-formula>
    here, for initial data which merely satisfy <jats:inline-formula>\r\n              <jats:alternatives>\r\n
    \               <jats:tex-math>$$u_0\\in W^{1,p+2}(\\Omega )$$</jats:tex-math>\r\n
    \               <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mrow>\r\n                    <mml:msub>\r\n                      <mml:mi>u</mml:mi>\r\n
    \                     <mml:mn>0</mml:mn>\r\n                    </mml:msub>\r\n
    \                   <mml:mo>∈</mml:mo>\r\n                    <mml:msup>\r\n                      <mml:mi>W</mml:mi>\r\n
    \                     <mml:mrow>\r\n                        <mml:mn>1</mml:mn>\r\n
    \                       <mml:mo>,</mml:mo>\r\n                        <mml:mi>p</mml:mi>\r\n
    \                       <mml:mo>+</mml:mo>\r\n                        <mml:mn>2</mml:mn>\r\n
    \                     </mml:mrow>\r\n                    </mml:msup>\r\n                    <mml:mrow>\r\n
    \                     <mml:mo>(</mml:mo>\r\n                      <mml:mi>Ω</mml:mi>\r\n
    \                     <mml:mo>)</mml:mo>\r\n                    </mml:mrow>\r\n
    \                 </mml:mrow>\r\n                </mml:math>\r\n              </jats:alternatives>\r\n
    \           </jats:inline-formula>, <jats:inline-formula>\r\n              <jats:alternatives>\r\n
    \               <jats:tex-math>$$u_{0t}\\in W^{1,p}(\\Omega )$$</jats:tex-math>\r\n
    \               <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mrow>\r\n                    <mml:msub>\r\n                      <mml:mi>u</mml:mi>\r\n
    \                     <mml:mrow>\r\n                        <mml:mn>0</mml:mn>\r\n
    \                       <mml:mi>t</mml:mi>\r\n                      </mml:mrow>\r\n
    \                   </mml:msub>\r\n                    <mml:mo>∈</mml:mo>\r\n
    \                   <mml:msup>\r\n                      <mml:mi>W</mml:mi>\r\n
    \                     <mml:mrow>\r\n                        <mml:mn>1</mml:mn>\r\n
    \                       <mml:mo>,</mml:mo>\r\n                        <mml:mi>p</mml:mi>\r\n
    \                     </mml:mrow>\r\n                    </mml:msup>\r\n                    <mml:mrow>\r\n
    \                     <mml:mo>(</mml:mo>\r\n                      <mml:mi>Ω</mml:mi>\r\n
    \                     <mml:mo>)</mml:mo>\r\n                    </mml:mrow>\r\n
    \                 </mml:mrow>\r\n                </mml:math>\r\n              </jats:alternatives>\r\n
    \           </jats:inline-formula> and <jats:inline-formula>\r\n              <jats:alternatives>\r\n
    \               <jats:tex-math>$$\\Theta _0\\in W^{1,p}(\\Omega )$$</jats:tex-math>\r\n
    \               <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mrow>\r\n                    <mml:msub>\r\n                      <mml:mi>Θ</mml:mi>\r\n
    \                     <mml:mn>0</mml:mn>\r\n                    </mml:msub>\r\n
    \                   <mml:mo>∈</mml:mo>\r\n                    <mml:msup>\r\n                      <mml:mi>W</mml:mi>\r\n
    \                     <mml:mrow>\r\n                        <mml:mn>1</mml:mn>\r\n
    \                       <mml:mo>,</mml:mo>\r\n                        <mml:mi>p</mml:mi>\r\n
    \                     </mml:mrow>\r\n                    </mml:msup>\r\n                    <mml:mrow>\r\n
    \                     <mml:mo>(</mml:mo>\r\n                      <mml:mi>Ω</mml:mi>\r\n
    \                     <mml:mo>)</mml:mo>\r\n                    </mml:mrow>\r\n
    \                 </mml:mrow>\r\n                </mml:math>\r\n              </jats:alternatives>\r\n
    \           </jats:inline-formula> with some <jats:inline-formula>\r\n              <jats:alternatives>\r\n
    \               <jats:tex-math>$$p\\ge 2$$</jats:tex-math>\r\n                <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n
    \                   <mml:mi>p</mml:mi>\r\n                    <mml:mo>≥</mml:mo>\r\n
    \                   <mml:mn>2</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math>\r\n
    \             </jats:alternatives>\r\n            </jats:inline-formula> such
    that <jats:inline-formula>\r\n              <jats:alternatives>\r\n                <jats:tex-math>$$p&gt;n$$</jats:tex-math>\r\n
    \               <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mrow>\r\n                    <mml:mi>p</mml:mi>\r\n                    <mml:mo>&gt;</mml:mo>\r\n
    \                   <mml:mi>n</mml:mi>\r\n                  </mml:mrow>\r\n                </mml:math>\r\n
    \             </jats:alternatives>\r\n            </jats:inline-formula>, a result
    on local-in-time existence and uniqueness is derived in a natural framework of
    weak solvability.</jats:p>"
article_number: '44'
author:
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Winkler M. Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity
    with Temperature-Dependent Parameters. <i>Applied Mathematics &#38;amp; Optimization</i>.
    2025;91(2). doi:<a href="https://doi.org/10.1007/s00245-025-10243-9">10.1007/s00245-025-10243-9</a>
  apa: Winkler, M. (2025). Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity
    with Temperature-Dependent Parameters. <i>Applied Mathematics &#38;amp; Optimization</i>,
    <i>91</i>(2), Article 44. <a href="https://doi.org/10.1007/s00245-025-10243-9">https://doi.org/10.1007/s00245-025-10243-9</a>
  bibtex: '@article{Winkler_2025, title={Rough Data in an Evolution System Generalizing
    1D Thermoviscoelasticity with Temperature-Dependent Parameters}, volume={91},
    DOI={<a href="https://doi.org/10.1007/s00245-025-10243-9">10.1007/s00245-025-10243-9</a>},
    number={244}, journal={Applied Mathematics &#38;amp; Optimization}, publisher={Springer
    Science and Business Media LLC}, author={Winkler, Michael}, year={2025} }'
  chicago: Winkler, Michael. “Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity
    with Temperature-Dependent Parameters.” <i>Applied Mathematics &#38;amp; Optimization</i>
    91, no. 2 (2025). <a href="https://doi.org/10.1007/s00245-025-10243-9">https://doi.org/10.1007/s00245-025-10243-9</a>.
  ieee: 'M. Winkler, “Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity
    with Temperature-Dependent Parameters,” <i>Applied Mathematics &#38;amp; Optimization</i>,
    vol. 91, no. 2, Art. no. 44, 2025, doi: <a href="https://doi.org/10.1007/s00245-025-10243-9">10.1007/s00245-025-10243-9</a>.'
  mla: Winkler, Michael. “Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity
    with Temperature-Dependent Parameters.” <i>Applied Mathematics &#38;amp; Optimization</i>,
    vol. 91, no. 2, 44, Springer Science and Business Media LLC, 2025, doi:<a href="https://doi.org/10.1007/s00245-025-10243-9">10.1007/s00245-025-10243-9</a>.
  short: M. Winkler, Applied Mathematics &#38;amp; Optimization 91 (2025).
date_created: 2025-12-18T20:20:06Z
date_updated: 2025-12-18T20:20:16Z
doi: 10.1007/s00245-025-10243-9
intvolume: '        91'
issue: '2'
language:
- iso: eng
publication: Applied Mathematics &amp; Optimization
publication_identifier:
  issn:
  - 0095-4616
  - 1432-0606
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with
  Temperature-Dependent Parameters
type: journal_article
user_id: '31496'
volume: 91
year: '2025'
...
---
_id: '63242'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n                  <jats:p>\r\n                    For\r\n
    \                   <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$p&gt;2$$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:mi>p</mml:mi>\r\n                            <mml:mo>&gt;</mml:mo>\r\n
    \                           <mml:mn>2</mml:mn>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    , the equation\r\n
    \                   <jats:disp-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$\\begin{aligned} u_t = u^p u_{xx}, \\qquad
    x\\in \\mathbb {R}, \\ t\\in \\mathbb {R}, \\end{aligned}$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mtable>\r\n
    \                             <mml:mtr>\r\n                                <mml:mtd>\r\n
    \                                 <mml:mrow>\r\n                                    <mml:msub>\r\n
    \                                     <mml:mi>u</mml:mi>\r\n                                      <mml:mi>t</mml:mi>\r\n
    \                                   </mml:msub>\r\n                                    <mml:mo>=</mml:mo>\r\n
    \                                   <mml:msup>\r\n                                      <mml:mi>u</mml:mi>\r\n
    \                                     <mml:mi>p</mml:mi>\r\n                                    </mml:msup>\r\n
    \                                   <mml:msub>\r\n                                      <mml:mi>u</mml:mi>\r\n
    \                                     <mml:mrow>\r\n                                        <mml:mi>xx</mml:mi>\r\n
    \                                     </mml:mrow>\r\n                                    </mml:msub>\r\n
    \                                   <mml:mo>,</mml:mo>\r\n                                    <mml:mspace/>\r\n
    \                                   <mml:mi>x</mml:mi>\r\n                                    <mml:mo>∈</mml:mo>\r\n
    \                                   <mml:mi>R</mml:mi>\r\n                                    <mml:mo>,</mml:mo>\r\n
    \                                   <mml:mspace/>\r\n                                    <mml:mi>t</mml:mi>\r\n
    \                                   <mml:mo>∈</mml:mo>\r\n                                    <mml:mi>R</mml:mi>\r\n
    \                                   <mml:mo>,</mml:mo>\r\n                                  </mml:mrow>\r\n
    \                               </mml:mtd>\r\n                              </mml:mtr>\r\n
    \                           </mml:mtable>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:disp-formula>\r\n                    is shown to admit
    positive and spatially increasing smooth solutions on all of\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$\\mathbb
    {R}\\times \\mathbb {R}$$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:mi>R</mml:mi>\r\n                            <mml:mo>×</mml:mo>\r\n
    \                           <mml:mi>R</mml:mi>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    which are precisely
    of the form of an accelerating wave for\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$t&lt;0$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mi>t</mml:mi>\r\n
    \                           <mml:mo>&lt;</mml:mo>\r\n                            <mml:mn>0</mml:mn>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   , and of a wave slowing down for\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$t&gt;0$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mi>t</mml:mi>\r\n
    \                           <mml:mo>&gt;</mml:mo>\r\n                            <mml:mn>0</mml:mn>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   . These solutions satisfy\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$u(\\cdot
    ,t)\\rightarrow 0$$</jats:tex-math>\r\n                        <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mi>u</mml:mi>\r\n
    \                           <mml:mo>(</mml:mo>\r\n                            <mml:mo>·</mml:mo>\r\n
    \                           <mml:mo>,</mml:mo>\r\n                            <mml:mi>t</mml:mi>\r\n
    \                           <mml:mo>)</mml:mo>\r\n                            <mml:mo>→</mml:mo>\r\n
    \                           <mml:mn>0</mml:mn>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    in\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$L^\\infty
    _{loc}(\\mathbb {R})$$</jats:tex-math>\r\n                        <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:msubsup>\r\n
    \                             <mml:mi>L</mml:mi>\r\n                              <mml:mrow>\r\n
    \                               <mml:mi>loc</mml:mi>\r\n                              </mml:mrow>\r\n
    \                             <mml:mi>∞</mml:mi>\r\n                            </mml:msubsup>\r\n
    \                           <mml:mrow>\r\n                              <mml:mo>(</mml:mo>\r\n
    \                             <mml:mi>R</mml:mi>\r\n                              <mml:mo>)</mml:mo>\r\n
    \                           </mml:mrow>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    as\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$t\\rightarrow
    + \\infty $$</jats:tex-math>\r\n                        <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mi>t</mml:mi>\r\n
    \                           <mml:mo>→</mml:mo>\r\n                            <mml:mo>+</mml:mo>\r\n
    \                           <mml:mi>∞</mml:mi>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    and as\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$t\\rightarrow
    -\\infty $$</jats:tex-math>\r\n                        <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mi>t</mml:mi>\r\n
    \                           <mml:mo>→</mml:mo>\r\n                            <mml:mo>-</mml:mo>\r\n
    \                           <mml:mi>∞</mml:mi>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    , and exhibit
    a yet apparently undiscovered phenomenon of transient rapid spatial growth, in
    the sense that\r\n                    <jats:disp-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$\\begin{aligned} \\lim _{x\\rightarrow
    +\\infty } x^{-1} u(x,t) \\quad \\text{ exists } \\text{ for } \\text{ all } t&lt;0,
    \\end{aligned}$$</jats:tex-math>\r\n                        <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mtable>\r\n
    \                             <mml:mtr>\r\n                                <mml:mtd>\r\n
    \                                 <mml:mrow>\r\n                                    <mml:munder>\r\n
    \                                     <mml:mo>lim</mml:mo>\r\n                                      <mml:mrow>\r\n
    \                                       <mml:mi>x</mml:mi>\r\n                                        <mml:mo>→</mml:mo>\r\n
    \                                       <mml:mo>+</mml:mo>\r\n                                        <mml:mi>∞</mml:mi>\r\n
    \                                     </mml:mrow>\r\n                                    </mml:munder>\r\n
    \                                   <mml:msup>\r\n                                      <mml:mi>x</mml:mi>\r\n
    \                                     <mml:mrow>\r\n                                        <mml:mo>-</mml:mo>\r\n
    \                                       <mml:mn>1</mml:mn>\r\n                                      </mml:mrow>\r\n
    \                                   </mml:msup>\r\n                                    <mml:mi>u</mml:mi>\r\n
    \                                   <mml:mrow>\r\n                                      <mml:mo>(</mml:mo>\r\n
    \                                     <mml:mi>x</mml:mi>\r\n                                      <mml:mo>,</mml:mo>\r\n
    \                                     <mml:mi>t</mml:mi>\r\n                                      <mml:mo>)</mml:mo>\r\n
    \                                   </mml:mrow>\r\n                                    <mml:mspace/>\r\n
    \                                   <mml:mspace/>\r\n                                    <mml:mtext>exists</mml:mtext>\r\n
    \                                   <mml:mspace/>\r\n                                    <mml:mspace/>\r\n
    \                                   <mml:mtext>for</mml:mtext>\r\n                                    <mml:mspace/>\r\n
    \                                   <mml:mspace/>\r\n                                    <mml:mtext>all</mml:mtext>\r\n
    \                                   <mml:mspace/>\r\n                                    <mml:mi>t</mml:mi>\r\n
    \                                   <mml:mo>&lt;</mml:mo>\r\n                                    <mml:mn>0</mml:mn>\r\n
    \                                   <mml:mo>,</mml:mo>\r\n                                  </mml:mrow>\r\n
    \                               </mml:mtd>\r\n                              </mml:mtr>\r\n
    \                           </mml:mtable>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:disp-formula>\r\n                    that\r\n                    <jats:disp-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$\\begin{aligned}
    \\lim _{x\\rightarrow +\\infty } x^{-\\frac{2}{p}} u(x,t) \\quad \\text{ exists
    } \\text{ for } \\text{ all } t&gt;0, \\end{aligned}$$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:mtable>\r\n                              <mml:mtr>\r\n
    \                               <mml:mtd>\r\n                                  <mml:mrow>\r\n
    \                                   <mml:munder>\r\n                                      <mml:mo>lim</mml:mo>\r\n
    \                                     <mml:mrow>\r\n                                        <mml:mi>x</mml:mi>\r\n
    \                                       <mml:mo>→</mml:mo>\r\n                                        <mml:mo>+</mml:mo>\r\n
    \                                       <mml:mi>∞</mml:mi>\r\n                                      </mml:mrow>\r\n
    \                                   </mml:munder>\r\n                                    <mml:msup>\r\n
    \                                     <mml:mi>x</mml:mi>\r\n                                      <mml:mrow>\r\n
    \                                       <mml:mo>-</mml:mo>\r\n                                        <mml:mfrac>\r\n
    \                                         <mml:mn>2</mml:mn>\r\n                                          <mml:mi>p</mml:mi>\r\n
    \                                       </mml:mfrac>\r\n                                      </mml:mrow>\r\n
    \                                   </mml:msup>\r\n                                    <mml:mi>u</mml:mi>\r\n
    \                                   <mml:mrow>\r\n                                      <mml:mo>(</mml:mo>\r\n
    \                                     <mml:mi>x</mml:mi>\r\n                                      <mml:mo>,</mml:mo>\r\n
    \                                     <mml:mi>t</mml:mi>\r\n                                      <mml:mo>)</mml:mo>\r\n
    \                                   </mml:mrow>\r\n                                    <mml:mspace/>\r\n
    \                                   <mml:mspace/>\r\n                                    <mml:mtext>exists</mml:mtext>\r\n
    \                                   <mml:mspace/>\r\n                                    <mml:mspace/>\r\n
    \                                   <mml:mtext>for</mml:mtext>\r\n                                    <mml:mspace/>\r\n
    \                                   <mml:mspace/>\r\n                                    <mml:mtext>all</mml:mtext>\r\n
    \                                   <mml:mspace/>\r\n                                    <mml:mi>t</mml:mi>\r\n
    \                                   <mml:mo>&gt;</mml:mo>\r\n                                    <mml:mn>0</mml:mn>\r\n
    \                                   <mml:mo>,</mml:mo>\r\n                                  </mml:mrow>\r\n
    \                               </mml:mtd>\r\n                              </mml:mtr>\r\n
    \                           </mml:mtable>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:disp-formula>\r\n                    but that\r\n                    <jats:disp-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$\\begin{aligned}
    u(x,0)=K e^{\\alpha x} \\qquad \\text{ for } \\text{ all } x\\in \\mathbb {R}\\end{aligned}$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mtable>\r\n
    \                             <mml:mtr>\r\n                                <mml:mtd>\r\n
    \                                 <mml:mrow>\r\n                                    <mml:mi>u</mml:mi>\r\n
    \                                   <mml:mrow>\r\n                                      <mml:mo>(</mml:mo>\r\n
    \                                     <mml:mi>x</mml:mi>\r\n                                      <mml:mo>,</mml:mo>\r\n
    \                                     <mml:mn>0</mml:mn>\r\n                                      <mml:mo>)</mml:mo>\r\n
    \                                   </mml:mrow>\r\n                                    <mml:mo>=</mml:mo>\r\n
    \                                   <mml:mi>K</mml:mi>\r\n                                    <mml:msup>\r\n
    \                                     <mml:mi>e</mml:mi>\r\n                                      <mml:mrow>\r\n
    \                                       <mml:mi>α</mml:mi>\r\n                                        <mml:mi>x</mml:mi>\r\n
    \                                     </mml:mrow>\r\n                                    </mml:msup>\r\n
    \                                   <mml:mspace/>\r\n                                    <mml:mspace/>\r\n
    \                                   <mml:mtext>for</mml:mtext>\r\n                                    <mml:mspace/>\r\n
    \                                   <mml:mspace/>\r\n                                    <mml:mtext>all</mml:mtext>\r\n
    \                                   <mml:mspace/>\r\n                                    <mml:mi>x</mml:mi>\r\n
    \                                   <mml:mo>∈</mml:mo>\r\n                                    <mml:mi>R</mml:mi>\r\n
    \                                 </mml:mrow>\r\n                                </mml:mtd>\r\n
    \                             </mml:mtr>\r\n                            </mml:mtable>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:disp-formula>\r\n
    \                   with some\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$K&gt;0$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mi>K</mml:mi>\r\n
    \                           <mml:mo>&gt;</mml:mo>\r\n                            <mml:mn>0</mml:mn>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   and\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$\\alpha &gt;0$$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:mi>α</mml:mi>\r\n                            <mml:mo>&gt;</mml:mo>\r\n
    \                           <mml:mn>0</mml:mn>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    .\r\n                  </jats:p>"
author:
- first_name: Celina
  full_name: Hanfland, Celina
  last_name: Hanfland
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Hanfland C, Winkler M. Exactly wave-type homoclinic orbits and emergence of
    transient exponential growth in a super-fast diffusion equation. <i>Journal of
    Elliptic and Parabolic Equations</i>. 2025;11(3):2041-2063. doi:<a href="https://doi.org/10.1007/s41808-025-00316-9">10.1007/s41808-025-00316-9</a>
  apa: Hanfland, C., &#38; Winkler, M. (2025). Exactly wave-type homoclinic orbits
    and emergence of transient exponential growth in a super-fast diffusion equation.
    <i>Journal of Elliptic and Parabolic Equations</i>, <i>11</i>(3), 2041–2063. <a
    href="https://doi.org/10.1007/s41808-025-00316-9">https://doi.org/10.1007/s41808-025-00316-9</a>
  bibtex: '@article{Hanfland_Winkler_2025, title={Exactly wave-type homoclinic orbits
    and emergence of transient exponential growth in a super-fast diffusion equation},
    volume={11}, DOI={<a href="https://doi.org/10.1007/s41808-025-00316-9">10.1007/s41808-025-00316-9</a>},
    number={3}, journal={Journal of Elliptic and Parabolic Equations}, publisher={Springer
    Science and Business Media LLC}, author={Hanfland, Celina and Winkler, Michael},
    year={2025}, pages={2041–2063} }'
  chicago: 'Hanfland, Celina, and Michael Winkler. “Exactly Wave-Type Homoclinic Orbits
    and Emergence of Transient Exponential Growth in a Super-Fast Diffusion Equation.”
    <i>Journal of Elliptic and Parabolic Equations</i> 11, no. 3 (2025): 2041–63.
    <a href="https://doi.org/10.1007/s41808-025-00316-9">https://doi.org/10.1007/s41808-025-00316-9</a>.'
  ieee: 'C. Hanfland and M. Winkler, “Exactly wave-type homoclinic orbits and emergence
    of transient exponential growth in a super-fast diffusion equation,” <i>Journal
    of Elliptic and Parabolic Equations</i>, vol. 11, no. 3, pp. 2041–2063, 2025,
    doi: <a href="https://doi.org/10.1007/s41808-025-00316-9">10.1007/s41808-025-00316-9</a>.'
  mla: Hanfland, Celina, and Michael Winkler. “Exactly Wave-Type Homoclinic Orbits
    and Emergence of Transient Exponential Growth in a Super-Fast Diffusion Equation.”
    <i>Journal of Elliptic and Parabolic Equations</i>, vol. 11, no. 3, Springer Science
    and Business Media LLC, 2025, pp. 2041–63, doi:<a href="https://doi.org/10.1007/s41808-025-00316-9">10.1007/s41808-025-00316-9</a>.
  short: C. Hanfland, M. Winkler, Journal of Elliptic and Parabolic Equations 11 (2025)
    2041–2063.
date_created: 2025-12-18T18:57:21Z
date_updated: 2025-12-18T20:16:49Z
doi: 10.1007/s41808-025-00316-9
intvolume: '        11'
issue: '3'
language:
- iso: eng
page: 2041-2063
publication: Journal of Elliptic and Parabolic Equations
publication_identifier:
  issn:
  - 2296-9020
  - 2296-9039
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Exactly wave-type homoclinic orbits and emergence of transient exponential
  growth in a super-fast diffusion equation
type: journal_article
user_id: '31496'
volume: 11
year: '2025'
...
---
_id: '63164'
abstract:
- lang: eng
  text: <jats:p> Refined investigation of chemotaxis processes has revealed a significant
    role of degeneracies in corresponding motilities in a number of application contexts.
    A rapidly growing literature concerned with the analysis of resulting mathematical
    models has been capable of solving fundamental issues, but various problems have
    remained open, or even newly arisen. The goal of the paper consists in a summary
    of some developments in this area, and particularly in the discussion of the question
    how far the introduction of degeneracies may influence the behavior of solutions
    to chemotaxis systems. </jats:p>
author:
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Winkler M. Effects of degeneracies in taxis-driven evolution. <i>Mathematical
    Models and Methods in Applied Sciences</i>. 2025;35(02):283-343. doi:<a href="https://doi.org/10.1142/s0218202525400020">10.1142/s0218202525400020</a>
  apa: Winkler, M. (2025). Effects of degeneracies in taxis-driven evolution. <i>Mathematical
    Models and Methods in Applied Sciences</i>, <i>35</i>(02), 283–343. <a href="https://doi.org/10.1142/s0218202525400020">https://doi.org/10.1142/s0218202525400020</a>
  bibtex: '@article{Winkler_2025, title={Effects of degeneracies in taxis-driven evolution},
    volume={35}, DOI={<a href="https://doi.org/10.1142/s0218202525400020">10.1142/s0218202525400020</a>},
    number={02}, journal={Mathematical Models and Methods in Applied Sciences}, publisher={World
    Scientific Pub Co Pte Ltd}, author={Winkler, Michael}, year={2025}, pages={283–343}
    }'
  chicago: 'Winkler, Michael. “Effects of Degeneracies in Taxis-Driven Evolution.”
    <i>Mathematical Models and Methods in Applied Sciences</i> 35, no. 02 (2025):
    283–343. <a href="https://doi.org/10.1142/s0218202525400020">https://doi.org/10.1142/s0218202525400020</a>.'
  ieee: 'M. Winkler, “Effects of degeneracies in taxis-driven evolution,” <i>Mathematical
    Models and Methods in Applied Sciences</i>, vol. 35, no. 02, pp. 283–343, 2025,
    doi: <a href="https://doi.org/10.1142/s0218202525400020">10.1142/s0218202525400020</a>.'
  mla: Winkler, Michael. “Effects of Degeneracies in Taxis-Driven Evolution.” <i>Mathematical
    Models and Methods in Applied Sciences</i>, vol. 35, no. 02, World Scientific
    Pub Co Pte Ltd, 2025, pp. 283–343, doi:<a href="https://doi.org/10.1142/s0218202525400020">10.1142/s0218202525400020</a>.
  short: M. Winkler, Mathematical Models and Methods in Applied Sciences 35 (2025)
    283–343.
date_created: 2025-12-16T19:23:40Z
date_updated: 2025-12-18T20:16:23Z
doi: 10.1142/s0218202525400020
intvolume: '        35'
issue: '02'
language:
- iso: eng
page: 283-343
publication: Mathematical Models and Methods in Applied Sciences
publication_identifier:
  issn:
  - 0218-2025
  - 1793-6314
publication_status: published
publisher: World Scientific Pub Co Pte Ltd
status: public
title: Effects of degeneracies in taxis-driven evolution
type: journal_article
user_id: '31496'
volume: 35
year: '2025'
...