---
_id: '45964'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n               <jats:p>Maximal parabolic
    $L^p$-regularity of linear parabolic equations on an evolving surface is shown
    by pulling back the problem to the initial surface and studying the maximal $L^p$-regularity
    on a fixed surface. By freezing the coefficients in the parabolic equations at
    a fixed time and utilizing a perturbation argument around the freezed time, it
    is shown that backward difference time discretizations of linear parabolic equations
    on an evolving surface along characteristic trajectories can preserve maximal
    $L^p$-regularity in the discrete setting. The result is applied to prove the stability
    and convergence of time discretizations of nonlinear parabolic equations on an
    evolving surface, with linearly implicit backward differentiation formulae characteristic
    trajectories of the surface, for general locally Lipschitz nonlinearities. The
    discrete maximal $L^p$-regularity is used to prove the boundedness and stability
    of numerical solutions in the $L^\\infty (0,T;W^{1,\\infty })$ norm, which is
    used to bound the nonlinear terms in the stability analysis. Optimal-order error
    estimates of time discretizations in the $L^\\infty (0,T;W^{1,\\infty })$ norm
    is obtained by combining the stability analysis with the consistency estimates.</jats:p>"
author:
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
- first_name: Buyang
  full_name: Li, Buyang
  last_name: Li
citation:
  ama: Kovács B, Li B. Maximal regularity of backward difference time discretization
    for evolving surface PDEs and its application to nonlinear problems. <i>IMA Journal
    of Numerical Analysis</i>. Published online 2022. doi:<a href="https://doi.org/10.1093/imanum/drac033">10.1093/imanum/drac033</a>
  apa: Kovács, B., &#38; Li, B. (2022). Maximal regularity of backward difference
    time discretization for evolving surface PDEs and its application to nonlinear
    problems. <i>IMA Journal of Numerical Analysis</i>. <a href="https://doi.org/10.1093/imanum/drac033">https://doi.org/10.1093/imanum/drac033</a>
  bibtex: '@article{Kovács_Li_2022, title={Maximal regularity of backward difference
    time discretization for evolving surface PDEs and its application to nonlinear
    problems}, DOI={<a href="https://doi.org/10.1093/imanum/drac033">10.1093/imanum/drac033</a>},
    journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press
    (OUP)}, author={Kovács, Balázs and Li, Buyang}, year={2022} }'
  chicago: Kovács, Balázs, and Buyang Li. “Maximal Regularity of Backward Difference
    Time Discretization for Evolving Surface PDEs and Its Application to Nonlinear
    Problems.” <i>IMA Journal of Numerical Analysis</i>, 2022. <a href="https://doi.org/10.1093/imanum/drac033">https://doi.org/10.1093/imanum/drac033</a>.
  ieee: 'B. Kovács and B. Li, “Maximal regularity of backward difference time discretization
    for evolving surface PDEs and its application to nonlinear problems,” <i>IMA Journal
    of Numerical Analysis</i>, 2022, doi: <a href="https://doi.org/10.1093/imanum/drac033">10.1093/imanum/drac033</a>.'
  mla: Kovács, Balázs, and Buyang Li. “Maximal Regularity of Backward Difference Time
    Discretization for Evolving Surface PDEs and Its Application to Nonlinear Problems.”
    <i>IMA Journal of Numerical Analysis</i>, Oxford University Press (OUP), 2022,
    doi:<a href="https://doi.org/10.1093/imanum/drac033">10.1093/imanum/drac033</a>.
  short: B. Kovács, B. Li, IMA Journal of Numerical Analysis (2022).
date_created: 2023-07-10T11:45:14Z
date_updated: 2024-04-03T09:17:59Z
department:
- _id: '841'
doi: 10.1093/imanum/drac033
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
publication: IMA Journal of Numerical Analysis
publication_identifier:
  issn:
  - 0272-4979
  - 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Maximal regularity of backward difference time discretization for evolving
  surface PDEs and its application to nonlinear problems
type: journal_article
user_id: '100441'
year: '2022'
...
---
_id: '45966'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n               <jats:p>This paper studies
    bulk–surface splitting methods of first order for (semilinear) parabolic partial
    differential equations with dynamic boundary conditions. The proposed Lie splitting
    scheme is based on a reformulation of the problem as a coupled partial differential–algebraic
    equation system, i.e., the boundary conditions are considered as a second dynamic
    equation that is coupled to the bulk problem. The splitting approach is combined
    with bulk–surface finite elements and an implicit Euler discretization of the
    two subsystems. We prove first-order convergence of the resulting fully discrete
    scheme in the presence of a weak CFL condition of the form $\\tau \\leqslant c
    h$ for some constant $c&amp;gt;0$. The convergence is also illustrated numerically
    using dynamic boundary conditions of Allen–Cahn type.</jats:p>"
author:
- first_name: Robert
  full_name: Altmann, Robert
  last_name: Altmann
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
- first_name: Christoph
  full_name: Zimmer, Christoph
  last_name: Zimmer
citation:
  ama: Altmann R, Kovács B, Zimmer C. Bulk–surface Lie splitting for parabolic problems
    with dynamic boundary conditions. <i>IMA Journal of Numerical Analysis</i>. 2022;43(2):950-975.
    doi:<a href="https://doi.org/10.1093/imanum/drac002">10.1093/imanum/drac002</a>
  apa: Altmann, R., Kovács, B., &#38; Zimmer, C. (2022). Bulk–surface Lie splitting
    for parabolic problems with dynamic boundary conditions. <i>IMA Journal of Numerical
    Analysis</i>, <i>43</i>(2), 950–975. <a href="https://doi.org/10.1093/imanum/drac002">https://doi.org/10.1093/imanum/drac002</a>
  bibtex: '@article{Altmann_Kovács_Zimmer_2022, title={Bulk–surface Lie splitting
    for parabolic problems with dynamic boundary conditions}, volume={43}, DOI={<a
    href="https://doi.org/10.1093/imanum/drac002">10.1093/imanum/drac002</a>}, number={2},
    journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press
    (OUP)}, author={Altmann, Robert and Kovács, Balázs and Zimmer, Christoph}, year={2022},
    pages={950–975} }'
  chicago: 'Altmann, Robert, Balázs Kovács, and Christoph Zimmer. “Bulk–Surface Lie
    Splitting for Parabolic Problems with Dynamic Boundary Conditions.” <i>IMA Journal
    of Numerical Analysis</i> 43, no. 2 (2022): 950–75. <a href="https://doi.org/10.1093/imanum/drac002">https://doi.org/10.1093/imanum/drac002</a>.'
  ieee: 'R. Altmann, B. Kovács, and C. Zimmer, “Bulk–surface Lie splitting for parabolic
    problems with dynamic boundary conditions,” <i>IMA Journal of Numerical Analysis</i>,
    vol. 43, no. 2, pp. 950–975, 2022, doi: <a href="https://doi.org/10.1093/imanum/drac002">10.1093/imanum/drac002</a>.'
  mla: Altmann, Robert, et al. “Bulk–Surface Lie Splitting for Parabolic Problems
    with Dynamic Boundary Conditions.” <i>IMA Journal of Numerical Analysis</i>, vol.
    43, no. 2, Oxford University Press (OUP), 2022, pp. 950–75, doi:<a href="https://doi.org/10.1093/imanum/drac002">10.1093/imanum/drac002</a>.
  short: R. Altmann, B. Kovács, C. Zimmer, IMA Journal of Numerical Analysis 43 (2022)
    950–975.
date_created: 2023-07-10T11:45:49Z
date_updated: 2024-04-03T09:16:47Z
department:
- _id: '841'
doi: 10.1093/imanum/drac002
intvolume: '        43'
issue: '2'
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
page: 950-975
publication: IMA Journal of Numerical Analysis
publication_identifier:
  issn:
  - 0272-4979
  - 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions
type: journal_article
user_id: '100441'
volume: 43
year: '2022'
...
---
_id: '45968'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n               <jats:p>We derive a numerical
    method, based on operator splitting, to abstract parabolic semilinear boundary
    coupled systems. The method decouples the linear components that describe the
    coupling and the dynamics in the abstract bulk- and surface-spaces, and treats
    the nonlinear terms similarly to an exponential integrator. The convergence proof
    is based on estimates for a recursive formulation of the error, using the parabolic
    smoothing property of analytic semigroups, and a careful comparison of the exact
    and approximate flows. This analysis also requires a deep understanding of the
    effects of the Dirichlet operator (the abstract version of the harmonic extension
    operator), which is essential for the stable coupling in our method. Numerical
    experiments, including problems with dynamic boundary conditions, reporting on
    convergence rates are presented.</jats:p>"
author:
- first_name: Petra
  full_name: Csomós, Petra
  last_name: Csomós
- first_name: Bálint
  full_name: Farkas, Bálint
  last_name: Farkas
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
citation:
  ama: Csomós P, Farkas B, Kovács B. Error estimates for a splitting integrator for
    abstract semilinear boundary coupled systems. <i>IMA Journal of Numerical Analysis</i>.
    Published online 2022. doi:<a href="https://doi.org/10.1093/imanum/drac079">10.1093/imanum/drac079</a>
  apa: Csomós, P., Farkas, B., &#38; Kovács, B. (2022). Error estimates for a splitting
    integrator for abstract semilinear boundary coupled systems. <i>IMA Journal of
    Numerical Analysis</i>. <a href="https://doi.org/10.1093/imanum/drac079">https://doi.org/10.1093/imanum/drac079</a>
  bibtex: '@article{Csomós_Farkas_Kovács_2022, title={Error estimates for a splitting
    integrator for abstract semilinear boundary coupled systems}, DOI={<a href="https://doi.org/10.1093/imanum/drac079">10.1093/imanum/drac079</a>},
    journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press
    (OUP)}, author={Csomós, Petra and Farkas, Bálint and Kovács, Balázs}, year={2022}
    }'
  chicago: Csomós, Petra, Bálint Farkas, and Balázs Kovács. “Error Estimates for a
    Splitting Integrator for Abstract Semilinear Boundary Coupled Systems.” <i>IMA
    Journal of Numerical Analysis</i>, 2022. <a href="https://doi.org/10.1093/imanum/drac079">https://doi.org/10.1093/imanum/drac079</a>.
  ieee: 'P. Csomós, B. Farkas, and B. Kovács, “Error estimates for a splitting integrator
    for abstract semilinear boundary coupled systems,” <i>IMA Journal of Numerical
    Analysis</i>, 2022, doi: <a href="https://doi.org/10.1093/imanum/drac079">10.1093/imanum/drac079</a>.'
  mla: Csomós, Petra, et al. “Error Estimates for a Splitting Integrator for Abstract
    Semilinear Boundary Coupled Systems.” <i>IMA Journal of Numerical Analysis</i>,
    Oxford University Press (OUP), 2022, doi:<a href="https://doi.org/10.1093/imanum/drac079">10.1093/imanum/drac079</a>.
  short: P. Csomós, B. Farkas, B. Kovács, IMA Journal of Numerical Analysis (2022).
date_created: 2023-07-10T11:46:54Z
date_updated: 2024-04-03T09:15:52Z
department:
- _id: '841'
doi: 10.1093/imanum/drac079
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
publication: IMA Journal of Numerical Analysis
publication_identifier:
  issn:
  - 0272-4979
  - 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Error estimates for a splitting integrator for abstract semilinear boundary
  coupled systems
type: journal_article
user_id: '100441'
year: '2022'
...
---
_id: '45958'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>In this paper, we consider a non-linear
    fourth-order evolution equation of Cahn–Hilliard-type on evolving surfaces with
    prescribed velocity, where the non-linear terms are only assumed to have locally
    Lipschitz derivatives. High-order evolving surface finite elements are used to
    discretise the weak equation system in space, and a modified matrix–vector formulation
    for the semi-discrete problem is derived. The anti-symmetric structure of the
    equation system is preserved by the spatial discretisation. A new stability proof,
    based on this structure, combined with consistency bounds proves optimal-order
    and uniform-in-time error estimates. The paper is concluded by a variety of numerical
    experiments.</jats:p>
author:
- first_name: Cedric Aaron
  full_name: Beschle, Cedric Aaron
  last_name: Beschle
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
citation:
  ama: Beschle CA, Kovács B. Stability and error estimates for non-linear Cahn–Hilliard-type
    equations on evolving surfaces. <i>Numerische Mathematik</i>. 2022;151(1):1-48.
    doi:<a href="https://doi.org/10.1007/s00211-022-01280-5">10.1007/s00211-022-01280-5</a>
  apa: Beschle, C. A., &#38; Kovács, B. (2022). Stability and error estimates for
    non-linear Cahn–Hilliard-type equations on evolving surfaces. <i>Numerische Mathematik</i>,
    <i>151</i>(1), 1–48. <a href="https://doi.org/10.1007/s00211-022-01280-5">https://doi.org/10.1007/s00211-022-01280-5</a>
  bibtex: '@article{Beschle_Kovács_2022, title={Stability and error estimates for
    non-linear Cahn–Hilliard-type equations on evolving surfaces}, volume={151}, DOI={<a
    href="https://doi.org/10.1007/s00211-022-01280-5">10.1007/s00211-022-01280-5</a>},
    number={1}, journal={Numerische Mathematik}, publisher={Springer Science and Business
    Media LLC}, author={Beschle, Cedric Aaron and Kovács, Balázs}, year={2022}, pages={1–48}
    }'
  chicago: 'Beschle, Cedric Aaron, and Balázs Kovács. “Stability and Error Estimates
    for Non-Linear Cahn–Hilliard-Type Equations on Evolving Surfaces.” <i>Numerische
    Mathematik</i> 151, no. 1 (2022): 1–48. <a href="https://doi.org/10.1007/s00211-022-01280-5">https://doi.org/10.1007/s00211-022-01280-5</a>.'
  ieee: 'C. A. Beschle and B. Kovács, “Stability and error estimates for non-linear
    Cahn–Hilliard-type equations on evolving surfaces,” <i>Numerische Mathematik</i>,
    vol. 151, no. 1, pp. 1–48, 2022, doi: <a href="https://doi.org/10.1007/s00211-022-01280-5">10.1007/s00211-022-01280-5</a>.'
  mla: Beschle, Cedric Aaron, and Balázs Kovács. “Stability and Error Estimates for
    Non-Linear Cahn–Hilliard-Type Equations on Evolving Surfaces.” <i>Numerische Mathematik</i>,
    vol. 151, no. 1, Springer Science and Business Media LLC, 2022, pp. 1–48, doi:<a
    href="https://doi.org/10.1007/s00211-022-01280-5">10.1007/s00211-022-01280-5</a>.
  short: C.A. Beschle, B. Kovács, Numerische Mathematik 151 (2022) 1–48.
date_created: 2023-07-10T11:43:44Z
date_updated: 2024-04-03T09:19:34Z
department:
- _id: '841'
doi: 10.1007/s00211-022-01280-5
intvolume: '       151'
issue: '1'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
page: 1-48
publication: Numerische Mathematik
publication_identifier:
  issn:
  - 0029-599X
  - 0945-3245
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Stability and error estimates for non-linear Cahn–Hilliard-type equations on
  evolving surfaces
type: journal_article
user_id: '100441'
volume: 151
year: '2022'
...
---
_id: '45956'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n               <jats:p>The full Maxwell
    equations in the unbounded three-dimensional space coupled to the Landau–Lifshitz–Gilbert
    equation serve as a well-tested model for ferromagnetic materials.\r\nWe propose
    a weak formulation of the coupled system based on the boundary integral formulation
    of the exterior Maxwell equations.\r\nWe show existence and partial uniqueness
    of a weak solution and propose a new numerical algorithm based on finite elements
    and boundary elements as spatial discretization with backward Euler and convolution
    quadrature for the time domain.\r\nThis is the first numerical algorithm which
    is able to deal with the coupled system of Landau–Lifshitz–Gilbert equation and
    full Maxwell’s equations without any simplifications like quasi-static approximations
    (e.g. eddy current model) and without restrictions on the shape of the domain
    (e.g. convexity).\r\nWe show well-posedness and convergence of the numerical algorithm
    under minimal assumptions on the regularity of the solution.\r\nThis is particularly
    important as there are few regularity results available and one generally expects
    the solution to be non-smooth.\r\nNumerical experiments illustrate and expand
    on the theoretical results.</jats:p>"
author:
- first_name: Jan
  full_name: Bohn, Jan
  last_name: Bohn
- first_name: Michael
  full_name: Feischl, Michael
  last_name: Feischl
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
citation:
  ama: 'Bohn J, Feischl M, Kovács B. FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert
    Equations via Convolution Quadrature: Weak Form and Numerical Approximation. <i>Computational
    Methods in Applied Mathematics</i>. 2022;23(1):19-48. doi:<a href="https://doi.org/10.1515/cmam-2022-0145">10.1515/cmam-2022-0145</a>'
  apa: 'Bohn, J., Feischl, M., &#38; Kovács, B. (2022). FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert
    Equations via Convolution Quadrature: Weak Form and Numerical Approximation. <i>Computational
    Methods in Applied Mathematics</i>, <i>23</i>(1), 19–48. <a href="https://doi.org/10.1515/cmam-2022-0145">https://doi.org/10.1515/cmam-2022-0145</a>'
  bibtex: '@article{Bohn_Feischl_Kovács_2022, title={FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert
    Equations via Convolution Quadrature: Weak Form and Numerical Approximation},
    volume={23}, DOI={<a href="https://doi.org/10.1515/cmam-2022-0145">10.1515/cmam-2022-0145</a>},
    number={1}, journal={Computational Methods in Applied Mathematics}, publisher={Walter
    de Gruyter GmbH}, author={Bohn, Jan and Feischl, Michael and Kovács, Balázs},
    year={2022}, pages={19–48} }'
  chicago: 'Bohn, Jan, Michael Feischl, and Balázs Kovács. “FEM-BEM Coupling for the
    Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form
    and Numerical Approximation.” <i>Computational Methods in Applied Mathematics</i>
    23, no. 1 (2022): 19–48. <a href="https://doi.org/10.1515/cmam-2022-0145">https://doi.org/10.1515/cmam-2022-0145</a>.'
  ieee: 'J. Bohn, M. Feischl, and B. Kovács, “FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert
    Equations via Convolution Quadrature: Weak Form and Numerical Approximation,”
    <i>Computational Methods in Applied Mathematics</i>, vol. 23, no. 1, pp. 19–48,
    2022, doi: <a href="https://doi.org/10.1515/cmam-2022-0145">10.1515/cmam-2022-0145</a>.'
  mla: 'Bohn, Jan, et al. “FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert
    Equations via Convolution Quadrature: Weak Form and Numerical Approximation.”
    <i>Computational Methods in Applied Mathematics</i>, vol. 23, no. 1, Walter de
    Gruyter GmbH, 2022, pp. 19–48, doi:<a href="https://doi.org/10.1515/cmam-2022-0145">10.1515/cmam-2022-0145</a>.'
  short: J. Bohn, M. Feischl, B. Kovács, Computational Methods in Applied Mathematics
    23 (2022) 19–48.
date_created: 2023-07-10T11:43:13Z
date_updated: 2024-04-03T09:20:30Z
department:
- _id: '841'
doi: 10.1515/cmam-2022-0145
intvolume: '        23'
issue: '1'
keyword:
- Applied Mathematics
- Computational Mathematics
- Numerical Analysis
language:
- iso: eng
page: 19-48
publication: Computational Methods in Applied Mathematics
publication_identifier:
  issn:
  - 1609-4840
  - 1609-9389
publication_status: published
publisher: Walter de Gruyter GmbH
status: public
title: 'FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution
  Quadrature: Weak Form and Numerical Approximation'
type: journal_article
user_id: '100441'
volume: 23
year: '2022'
...
---
_id: '53174'
author:
- first_name: Ina
  full_name: Krause, Ina
  id: '105654'
  last_name: Krause
  orcid: 0000-0003-0170-7713
citation:
  ama: 'Krause I. Distanzarbeit als Impulsgeber beruflicher Weiterbildung. Zur Bedeutung
    von neuen Schlüsselkompetenzen und Weiterbildung im Strukturwandels von Büroarbeitswelten
    in und nach der Corona-Pandemie. In: Bellmann L, Ertl H, Gerhards C, Sloane P,
    eds. <i>ZBW-Beiheft: Betriebliche Berufsbildungsforschung</i>. ; 2022.'
  apa: 'Krause, I. (2022). Distanzarbeit als Impulsgeber beruflicher Weiterbildung.
    Zur Bedeutung von neuen Schlüsselkompetenzen und Weiterbildung im Strukturwandels
    von Büroarbeitswelten in und nach der Corona-Pandemie. In L. Bellmann, H. Ertl,
    C. Gerhards, &#38; P. Sloane (Eds.), <i>ZBW-Beiheft: Betriebliche Berufsbildungsforschung</i>.'
  bibtex: '@inbook{Krause_2022, title={Distanzarbeit als Impulsgeber beruflicher Weiterbildung.
    Zur Bedeutung von neuen Schlüsselkompetenzen und Weiterbildung im Strukturwandels
    von Büroarbeitswelten in und nach der Corona-Pandemie}, booktitle={ZBW-Beiheft:
    Betriebliche Berufsbildungsforschung}, author={Krause, Ina}, editor={Bellmann,
    Lutz  and Ertl, Hubert and Gerhards, Christian and Sloane, Peter}, year={2022}
    }'
  chicago: 'Krause, Ina. “Distanzarbeit Als Impulsgeber Beruflicher Weiterbildung.
    Zur Bedeutung von Neuen Schlüsselkompetenzen Und Weiterbildung Im Strukturwandels
    von Büroarbeitswelten in Und Nach Der Corona-Pandemie.” In <i>ZBW-Beiheft: Betriebliche
    Berufsbildungsforschung</i>, edited by Lutz  Bellmann, Hubert Ertl, Christian
    Gerhards, and Peter Sloane, 2022.'
  ieee: 'I. Krause, “Distanzarbeit als Impulsgeber beruflicher Weiterbildung. Zur
    Bedeutung von neuen Schlüsselkompetenzen und Weiterbildung im Strukturwandels
    von Büroarbeitswelten in und nach der Corona-Pandemie,” in <i>ZBW-Beiheft: Betriebliche
    Berufsbildungsforschung</i>, L. Bellmann, H. Ertl, C. Gerhards, and P. Sloane,
    Eds. 2022.'
  mla: 'Krause, Ina. “Distanzarbeit Als Impulsgeber Beruflicher Weiterbildung. Zur
    Bedeutung von Neuen Schlüsselkompetenzen Und Weiterbildung Im Strukturwandels
    von Büroarbeitswelten in Und Nach Der Corona-Pandemie.” <i>ZBW-Beiheft: Betriebliche
    Berufsbildungsforschung</i>, edited by Lutz  Bellmann et al., 2022.'
  short: 'I. Krause, in: L. Bellmann, H. Ertl, C. Gerhards, P. Sloane (Eds.), ZBW-Beiheft:
    Betriebliche Berufsbildungsforschung, 2022.'
date_created: 2024-04-03T11:27:03Z
date_updated: 2024-04-03T11:27:18Z
editor:
- first_name: 'Lutz '
  full_name: 'Bellmann, Lutz '
  last_name: Bellmann
- first_name: Hubert
  full_name: Ertl, Hubert
  last_name: Ertl
- first_name: Christian
  full_name: Gerhards, Christian
  last_name: Gerhards
- first_name: Peter
  full_name: Sloane, Peter
  last_name: Sloane
language:
- iso: eng
publication: 'ZBW-Beiheft: Betriebliche Berufsbildungsforschung'
status: public
title: Distanzarbeit als Impulsgeber beruflicher Weiterbildung. Zur Bedeutung von
  neuen Schlüsselkompetenzen und Weiterbildung im Strukturwandels von Büroarbeitswelten
  in und nach der Corona-Pandemie
type: book_chapter
user_id: '105654'
year: '2022'
...
---
_id: '33740'
author:
- first_name: N'Dah Jean
  full_name: KOUAGOU, N'Dah Jean
  id: '87189'
  last_name: KOUAGOU
- first_name: Stefan
  full_name: Heindorf, Stefan
  id: '11871'
  last_name: Heindorf
  orcid: 0000-0002-4525-6865
- first_name: Caglar
  full_name: Demir, Caglar
  id: '43817'
  last_name: Demir
- first_name: Axel-Cyrille
  full_name: Ngonga Ngomo, Axel-Cyrille
  id: '65716'
  last_name: Ngonga Ngomo
citation:
  ama: 'KOUAGOU NJ, Heindorf S, Demir C, Ngonga Ngomo A-C. Learning Concept Lengths
    Accelerates Concept Learning in ALC. In: <i>The Semantic Web</i>. Springer International
    Publishing; 2022. doi:<a href="https://doi.org/10.1007/978-3-031-06981-9_14">10.1007/978-3-031-06981-9_14</a>'
  apa: KOUAGOU, N. J., Heindorf, S., Demir, C., &#38; Ngonga Ngomo, A.-C. (2022).
    Learning Concept Lengths Accelerates Concept Learning in ALC. In <i>The Semantic
    Web</i>. Springer International Publishing. <a href="https://doi.org/10.1007/978-3-031-06981-9_14">https://doi.org/10.1007/978-3-031-06981-9_14</a>
  bibtex: '@inbook{KOUAGOU_Heindorf_Demir_Ngonga Ngomo_2022, place={Cham}, title={Learning
    Concept Lengths Accelerates Concept Learning in ALC}, DOI={<a href="https://doi.org/10.1007/978-3-031-06981-9_14">10.1007/978-3-031-06981-9_14</a>},
    booktitle={The Semantic Web}, publisher={Springer International Publishing}, author={KOUAGOU,
    N’Dah Jean and Heindorf, Stefan and Demir, Caglar and Ngonga Ngomo, Axel-Cyrille},
    year={2022} }'
  chicago: 'KOUAGOU, N’Dah Jean, Stefan Heindorf, Caglar Demir, and Axel-Cyrille Ngonga
    Ngomo. “Learning Concept Lengths Accelerates Concept Learning in ALC.” In <i>The
    Semantic Web</i>. Cham: Springer International Publishing, 2022. <a href="https://doi.org/10.1007/978-3-031-06981-9_14">https://doi.org/10.1007/978-3-031-06981-9_14</a>.'
  ieee: 'N. J. KOUAGOU, S. Heindorf, C. Demir, and A.-C. Ngonga Ngomo, “Learning Concept
    Lengths Accelerates Concept Learning in ALC,” in <i>The Semantic Web</i>, Cham:
    Springer International Publishing, 2022.'
  mla: KOUAGOU, N’Dah Jean, et al. “Learning Concept Lengths Accelerates Concept Learning
    in ALC.” <i>The Semantic Web</i>, Springer International Publishing, 2022, doi:<a
    href="https://doi.org/10.1007/978-3-031-06981-9_14">10.1007/978-3-031-06981-9_14</a>.
  short: 'N.J. KOUAGOU, S. Heindorf, C. Demir, A.-C. Ngonga Ngomo, in: The Semantic
    Web, Springer International Publishing, Cham, 2022.'
date_created: 2022-10-15T19:34:41Z
date_updated: 2024-04-03T13:26:10Z
department:
- _id: '574'
- _id: '760'
doi: 10.1007/978-3-031-06981-9_14
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2107.04911
oa: '1'
place: Cham
publication: The Semantic Web
publication_identifier:
  isbn:
  - '9783031069802'
  - '9783031069819'
  issn:
  - 0302-9743
  - 1611-3349
publication_status: published
publisher: Springer International Publishing
related_material:
  link:
  - relation: confirmation
    url: https://link.springer.com/chapter/10.1007/978-3-031-06981-9_14
status: public
title: Learning Concept Lengths Accelerates Concept Learning in ALC
type: book_chapter
user_id: '11871'
year: '2022'
...
---
_id: '53266'
author:
- first_name: Mohammad
  full_name: Soleymani, Mohammad
  last_name: Soleymani
- first_name: Ignacio
  full_name: Santamaria, Ignacio
  last_name: Santamaria
- first_name: Eduard A.
  full_name: Jorswieck, Eduard A.
  last_name: Jorswieck
citation:
  ama: Soleymani M, Santamaria I, Jorswieck EA. Rate Splitting in MIMO RIS-Assisted
    Systems With Hardware Impairments and Improper Signaling. <i>IEEE Transactions
    on Vehicular Technology</i>. 2022;72(4):4580-4597. doi:<a href="https://doi.org/10.1109/tvt.2022.3222633">10.1109/tvt.2022.3222633</a>
  apa: Soleymani, M., Santamaria, I., &#38; Jorswieck, E. A. (2022). Rate Splitting
    in MIMO RIS-Assisted Systems With Hardware Impairments and Improper Signaling.
    <i>IEEE Transactions on Vehicular Technology</i>, <i>72</i>(4), 4580–4597. <a
    href="https://doi.org/10.1109/tvt.2022.3222633">https://doi.org/10.1109/tvt.2022.3222633</a>
  bibtex: '@article{Soleymani_Santamaria_Jorswieck_2022, title={Rate Splitting in
    MIMO RIS-Assisted Systems With Hardware Impairments and Improper Signaling}, volume={72},
    DOI={<a href="https://doi.org/10.1109/tvt.2022.3222633">10.1109/tvt.2022.3222633</a>},
    number={4}, journal={IEEE Transactions on Vehicular Technology}, publisher={Institute
    of Electrical and Electronics Engineers (IEEE)}, author={Soleymani, Mohammad and
    Santamaria, Ignacio and Jorswieck, Eduard A.}, year={2022}, pages={4580–4597}
    }'
  chicago: 'Soleymani, Mohammad, Ignacio Santamaria, and Eduard A. Jorswieck. “Rate
    Splitting in MIMO RIS-Assisted Systems With Hardware Impairments and Improper
    Signaling.” <i>IEEE Transactions on Vehicular Technology</i> 72, no. 4 (2022):
    4580–97. <a href="https://doi.org/10.1109/tvt.2022.3222633">https://doi.org/10.1109/tvt.2022.3222633</a>.'
  ieee: 'M. Soleymani, I. Santamaria, and E. A. Jorswieck, “Rate Splitting in MIMO
    RIS-Assisted Systems With Hardware Impairments and Improper Signaling,” <i>IEEE
    Transactions on Vehicular Technology</i>, vol. 72, no. 4, pp. 4580–4597, 2022,
    doi: <a href="https://doi.org/10.1109/tvt.2022.3222633">10.1109/tvt.2022.3222633</a>.'
  mla: Soleymani, Mohammad, et al. “Rate Splitting in MIMO RIS-Assisted Systems With
    Hardware Impairments and Improper Signaling.” <i>IEEE Transactions on Vehicular
    Technology</i>, vol. 72, no. 4, Institute of Electrical and Electronics Engineers
    (IEEE), 2022, pp. 4580–97, doi:<a href="https://doi.org/10.1109/tvt.2022.3222633">10.1109/tvt.2022.3222633</a>.
  short: M. Soleymani, I. Santamaria, E.A. Jorswieck, IEEE Transactions on Vehicular
    Technology 72 (2022) 4580–4597.
date_created: 2024-04-05T09:04:01Z
date_updated: 2024-04-05T13:21:31Z
department:
- _id: '263'
doi: 10.1109/tvt.2022.3222633
intvolume: '        72'
issue: '4'
keyword:
- Electrical and Electronic Engineering
- Computer Networks and Communications
- Aerospace Engineering
- Automotive Engineering
language:
- iso: eng
page: 4580-4597
publication: IEEE Transactions on Vehicular Technology
publication_identifier:
  issn:
  - 0018-9545
  - 1939-9359
publication_status: published
publisher: Institute of Electrical and Electronics Engineers (IEEE)
status: public
title: Rate Splitting in MIMO RIS-Assisted Systems With Hardware Impairments and Improper
  Signaling
type: journal_article
user_id: '67076'
volume: 72
year: '2022'
...
---
_id: '53267'
author:
- first_name: Mohammad
  full_name: Soleymani, Mohammad
  last_name: Soleymani
- first_name: Ignacio
  full_name: Santamaria, Ignacio
  last_name: Santamaria
- first_name: Peter J.
  full_name: Schreier, Peter J.
  last_name: Schreier
citation:
  ama: Soleymani M, Santamaria I, Schreier PJ. Improper Signaling for Multicell MIMO
    RIS-Assisted Broadcast Channels With I/Q Imbalance. <i>IEEE Transactions on Green
    Communications and Networking</i>. 2022;6(2):723-738. doi:<a href="https://doi.org/10.1109/tgcn.2021.3140150">10.1109/tgcn.2021.3140150</a>
  apa: Soleymani, M., Santamaria, I., &#38; Schreier, P. J. (2022). Improper Signaling
    for Multicell MIMO RIS-Assisted Broadcast Channels With I/Q Imbalance. <i>IEEE
    Transactions on Green Communications and Networking</i>, <i>6</i>(2), 723–738.
    <a href="https://doi.org/10.1109/tgcn.2021.3140150">https://doi.org/10.1109/tgcn.2021.3140150</a>
  bibtex: '@article{Soleymani_Santamaria_Schreier_2022, title={Improper Signaling
    for Multicell MIMO RIS-Assisted Broadcast Channels With I/Q Imbalance}, volume={6},
    DOI={<a href="https://doi.org/10.1109/tgcn.2021.3140150">10.1109/tgcn.2021.3140150</a>},
    number={2}, journal={IEEE Transactions on Green Communications and Networking},
    publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Soleymani,
    Mohammad and Santamaria, Ignacio and Schreier, Peter J.}, year={2022}, pages={723–738}
    }'
  chicago: 'Soleymani, Mohammad, Ignacio Santamaria, and Peter J. Schreier. “Improper
    Signaling for Multicell MIMO RIS-Assisted Broadcast Channels With I/Q Imbalance.”
    <i>IEEE Transactions on Green Communications and Networking</i> 6, no. 2 (2022):
    723–38. <a href="https://doi.org/10.1109/tgcn.2021.3140150">https://doi.org/10.1109/tgcn.2021.3140150</a>.'
  ieee: 'M. Soleymani, I. Santamaria, and P. J. Schreier, “Improper Signaling for
    Multicell MIMO RIS-Assisted Broadcast Channels With I/Q Imbalance,” <i>IEEE Transactions
    on Green Communications and Networking</i>, vol. 6, no. 2, pp. 723–738, 2022,
    doi: <a href="https://doi.org/10.1109/tgcn.2021.3140150">10.1109/tgcn.2021.3140150</a>.'
  mla: Soleymani, Mohammad, et al. “Improper Signaling for Multicell MIMO RIS-Assisted
    Broadcast Channels With I/Q Imbalance.” <i>IEEE Transactions on Green Communications
    and Networking</i>, vol. 6, no. 2, Institute of Electrical and Electronics Engineers
    (IEEE), 2022, pp. 723–38, doi:<a href="https://doi.org/10.1109/tgcn.2021.3140150">10.1109/tgcn.2021.3140150</a>.
  short: M. Soleymani, I. Santamaria, P.J. Schreier, IEEE Transactions on Green Communications
    and Networking 6 (2022) 723–738.
date_created: 2024-04-05T09:04:25Z
date_updated: 2024-04-05T13:21:41Z
department:
- _id: '263'
doi: 10.1109/tgcn.2021.3140150
intvolume: '         6'
issue: '2'
keyword:
- Computer Networks and Communications
- Renewable Energy
- Sustainability and the Environment
language:
- iso: eng
page: 723-738
publication: IEEE Transactions on Green Communications and Networking
publication_identifier:
  issn:
  - 2473-2400
publication_status: published
publisher: Institute of Electrical and Electronics Engineers (IEEE)
status: public
title: Improper Signaling for Multicell MIMO RIS-Assisted Broadcast Channels With
  I/Q Imbalance
type: journal_article
user_id: '67076'
volume: 6
year: '2022'
...
---
_id: '53306'
author:
- first_name: Hassan Ghasemzadeh
  full_name: Mohammadi, Hassan Ghasemzadeh
  last_name: Mohammadi
- first_name: Felix Paul
  full_name: Jentzsch, Felix Paul
  last_name: Jentzsch
- first_name: Maurice
  full_name: Kuschel, Maurice
  id: '56070'
  last_name: Kuschel
- first_name: Rahil
  full_name: Arshad, Rahil
  last_name: Arshad
- first_name: Sneha
  full_name: Rautmare, Sneha
  last_name: Rautmare
- first_name: Suraj
  full_name: Manjunatha, Suraj
  last_name: Manjunatha
- first_name: Marco
  full_name: Platzner, Marco
  last_name: Platzner
- first_name: Alexander
  full_name: Boschmann, Alexander
  last_name: Boschmann
- first_name: Dirk
  full_name: Schollbach, Dirk
  last_name: Schollbach
citation:
  ama: 'Mohammadi HG, Jentzsch FP, Kuschel M, et al. FLight: FPGA Acceleration of
    Lightweight DNN Model Inference in Industrial Analytics. In: <i>Communications
    in Computer and Information Science</i>. Springer International Publishing; 2022.
    doi:<a href="https://doi.org/10.1007/978-3-030-93736-2_27">10.1007/978-3-030-93736-2_27</a>'
  apa: 'Mohammadi, H. G., Jentzsch, F. P., Kuschel, M., Arshad, R., Rautmare, S.,
    Manjunatha, S., Platzner, M., Boschmann, A., &#38; Schollbach, D. (2022). FLight:
    FPGA Acceleration of Lightweight DNN Model Inference in Industrial Analytics.
    In <i>Communications in Computer and Information Science</i>. Springer International
    Publishing. <a href="https://doi.org/10.1007/978-3-030-93736-2_27">https://doi.org/10.1007/978-3-030-93736-2_27</a>'
  bibtex: '@inbook{Mohammadi_Jentzsch_Kuschel_Arshad_Rautmare_Manjunatha_Platzner_Boschmann_Schollbach_2022,
    place={Cham}, title={FLight: FPGA Acceleration of Lightweight DNN Model Inference
    in Industrial Analytics}, DOI={<a href="https://doi.org/10.1007/978-3-030-93736-2_27">10.1007/978-3-030-93736-2_27</a>},
    booktitle={Communications in Computer and Information Science}, publisher={Springer
    International Publishing}, author={Mohammadi, Hassan Ghasemzadeh and Jentzsch,
    Felix Paul and Kuschel, Maurice and Arshad, Rahil and Rautmare, Sneha and Manjunatha,
    Suraj and Platzner, Marco and Boschmann, Alexander and Schollbach, Dirk}, year={2022}
    }'
  chicago: 'Mohammadi, Hassan Ghasemzadeh, Felix Paul Jentzsch, Maurice Kuschel, Rahil
    Arshad, Sneha Rautmare, Suraj Manjunatha, Marco Platzner, Alexander Boschmann,
    and Dirk Schollbach. “FLight: FPGA Acceleration of Lightweight DNN Model Inference
    in Industrial Analytics.” In <i>Communications in Computer and Information Science</i>.
    Cham: Springer International Publishing, 2022. <a href="https://doi.org/10.1007/978-3-030-93736-2_27">https://doi.org/10.1007/978-3-030-93736-2_27</a>.'
  ieee: 'H. G. Mohammadi <i>et al.</i>, “FLight: FPGA Acceleration of Lightweight
    DNN Model Inference in Industrial Analytics,” in <i>Communications in Computer
    and Information Science</i>, Cham: Springer International Publishing, 2022.'
  mla: 'Mohammadi, Hassan Ghasemzadeh, et al. “FLight: FPGA Acceleration of Lightweight
    DNN Model Inference in Industrial Analytics.” <i>Communications in Computer and
    Information Science</i>, Springer International Publishing, 2022, doi:<a href="https://doi.org/10.1007/978-3-030-93736-2_27">10.1007/978-3-030-93736-2_27</a>.'
  short: 'H.G. Mohammadi, F.P. Jentzsch, M. Kuschel, R. Arshad, S. Rautmare, S. Manjunatha,
    M. Platzner, A. Boschmann, D. Schollbach, in: Communications in Computer and Information
    Science, Springer International Publishing, Cham, 2022.'
date_created: 2024-04-05T14:43:07Z
date_updated: 2024-04-05T14:50:26Z
doi: 10.1007/978-3-030-93736-2_27
language:
- iso: eng
place: Cham
publication: Communications in Computer and Information Science
publication_identifier:
  isbn:
  - '9783030937355'
  - '9783030937362'
  issn:
  - 1865-0929
  - 1865-0937
publication_status: published
publisher: Springer International Publishing
status: public
title: 'FLight: FPGA Acceleration of Lightweight DNN Model Inference in Industrial
  Analytics'
type: book_chapter
user_id: '56070'
year: '2022'
...
---
_id: '53319'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n               <jats:p>The Neumann problem
    for (0.1)$$ \\begin{align}&amp; V_t = \\Delta V-aV+f(x,t) \\end{align}$$is considered
    in bounded domains $\\Omega \\subset {\\mathbb {R}}^n$ with smooth boundary, where
    $n\\ge 1$ and $a\\in {\\mathbb {R}}$. By means of a variational approach, a statement
    on boundedness of the quantities $$ \\begin{eqnarray*} \\sup_{t\\in (0,T)} \\int_\\Omega
    \\big|\\nabla V(\\cdot,t)\\big|^p L^{\\frac{n+p}{n+2}} \\Big( \\big|\\nabla V(\\cdot,t)\\big|
    \\Big) \\end{eqnarray*}$$in dependence on the expressions (0.2)$$ \\begin{align}&amp;
    \\sup_{t\\in (0,T-\\tau)} \\int_t^{t+\\tau} \\int_\\Omega |f|^{\\frac{(n+2)p}{n+p}}
    L\\big( |f|\\big) \\end{align}$$is derived for $p\\ge 2$, $\\tau&amp;gt;0$, and
    $T\\ge 2\\tau $, provided that $L\\in C^0([0,\\infty ))$ is positive, strictly
    increasing, unbounded, and slowly growing in the sense that $\\limsup _{s\\to
    \\infty } \\frac {L(s^{\\lambda _0})}{L(s)} &amp;lt;\\infty $ for some $\\lambda
    _0&amp;gt;1$. In the particular case when $p=n\\ge 2$, an additional condition
    on growth of $L$, particularly satisfied by $L(\\xi ):=\\ln ^\\alpha (\\xi +b)$
    whenever $b&amp;gt;0$ and $\\alpha&amp;gt;\\frac {(n+2)(n-1)}{2n}$, is identified
    as sufficient to ensure that as a consequence of the above, bounds for theintegrals
    in (0.2) even imply estimates for the spatio-temporal modulus of continuity of
    solutions to (0.1). A subsequent application to the Keller–Segel system $$ \\begin{eqnarray*}
    \\left\\{ \\begin{array}{l} u_t = \\nabla \\cdot \\big( D(v)\\nabla u\\big) -
    \\nabla \\cdot \\big( uS(v)\\nabla v\\big) + ru - \\mu u^2, \\\\[1mm] v_t = \\Delta
    v-v+u, \\end{array} \\right. \\end{eqnarray*}$$shows that when $n=2$, $r\\in {\\mathbb
    {R}}$, $0&amp;lt;D\\in C^2([0,\\infty ))$, and $S\\in C^2([0,\\infty )) \\cap
    W^{1,\\infty }((0,\\infty ))$ and thus especially in the presence of arbitrarily
    strong diffusion degeneracies implied by rapid decay of $D$, any choice of $\\mu&amp;gt;0$
    excludes blowup in the sense that for all suitably regular nonnegative initial
    data, an associated initial-boundary value problem admits a global bounded classical
    solution.</jats:p>"
author:
- first_name: Michael
  full_name: Winkler, Michael
  last_name: Winkler
citation:
  ama: Winkler M. A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application
    to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion
    System. <i>International Mathematics Research Notices</i>. 2022;2023(19):16336-16393.
    doi:<a href="https://doi.org/10.1093/imrn/rnac286">10.1093/imrn/rnac286</a>
  apa: Winkler, M. (2022). A Result on Parabolic Gradient Regularity in Orlicz Spaces
    and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type
    Cross-Diffusion System. <i>International Mathematics Research Notices</i>, <i>2023</i>(19),
    16336–16393. <a href="https://doi.org/10.1093/imrn/rnac286">https://doi.org/10.1093/imrn/rnac286</a>
  bibtex: '@article{Winkler_2022, title={A Result on Parabolic Gradient Regularity
    in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a
    Keller–Segel-Type Cross-Diffusion System}, volume={2023}, DOI={<a href="https://doi.org/10.1093/imrn/rnac286">10.1093/imrn/rnac286</a>},
    number={19}, journal={International Mathematics Research Notices}, publisher={Oxford
    University Press (OUP)}, author={Winkler, Michael}, year={2022}, pages={16336–16393}
    }'
  chicago: 'Winkler, Michael. “A Result on Parabolic Gradient Regularity in Orlicz
    Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type
    Cross-Diffusion System.” <i>International Mathematics Research Notices</i> 2023,
    no. 19 (2022): 16336–93. <a href="https://doi.org/10.1093/imrn/rnac286">https://doi.org/10.1093/imrn/rnac286</a>.'
  ieee: 'M. Winkler, “A Result on Parabolic Gradient Regularity in Orlicz Spaces and
    Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion
    System,” <i>International Mathematics Research Notices</i>, vol. 2023, no. 19,
    pp. 16336–16393, 2022, doi: <a href="https://doi.org/10.1093/imrn/rnac286">10.1093/imrn/rnac286</a>.'
  mla: Winkler, Michael. “A Result on Parabolic Gradient Regularity in Orlicz Spaces
    and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type
    Cross-Diffusion System.” <i>International Mathematics Research Notices</i>, vol.
    2023, no. 19, Oxford University Press (OUP), 2022, pp. 16336–93, doi:<a href="https://doi.org/10.1093/imrn/rnac286">10.1093/imrn/rnac286</a>.
  short: M. Winkler, International Mathematics Research Notices 2023 (2022) 16336–16393.
date_created: 2024-04-07T12:33:44Z
date_updated: 2024-04-07T12:36:06Z
doi: 10.1093/imrn/rnac286
intvolume: '      2023'
issue: '19'
keyword:
- General Mathematics
language:
- iso: eng
page: 16336-16393
publication: International Mathematics Research Notices
publication_identifier:
  issn:
  - 1073-7928
  - 1687-0247
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application
  to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion
  System
type: journal_article
user_id: '31496'
volume: 2023
year: '2022'
...
---
_id: '53321'
abstract:
- lang: eng
  text: '<jats:p> The chemotaxis system [Formula: see text] is considered in a ball
    [Formula: see text], [Formula: see text], where the positive function [Formula:
    see text] reflects suitably weak diffusion by satisfying [Formula: see text] for
    some [Formula: see text]. It is shown that whenever [Formula: see text] is positive
    and satisfies [Formula: see text] as [Formula: see text], one can find a suitably
    regular nonlinearity [Formula: see text] with the property that at each sufficiently
    large mass level [Formula: see text] there exists a globally defined radially
    symmetric classical solution to a Neumann-type boundary value problem for (⋆)
    which satisfies [Formula: see text] </jats:p>'
author:
- first_name: Michael
  full_name: Winkler, Michael
  last_name: Winkler
citation:
  ama: Winkler M. Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems.
    <i>Communications in Contemporary Mathematics</i>. 2022;25(10). doi:<a href="https://doi.org/10.1142/s0219199722500626">10.1142/s0219199722500626</a>
  apa: Winkler, M. (2022). Arbitrarily fast grow-up rates in quasilinear Keller–Segel
    systems. <i>Communications in Contemporary Mathematics</i>, <i>25</i>(10). <a
    href="https://doi.org/10.1142/s0219199722500626">https://doi.org/10.1142/s0219199722500626</a>
  bibtex: '@article{Winkler_2022, title={Arbitrarily fast grow-up rates in quasilinear
    Keller–Segel systems}, volume={25}, DOI={<a href="https://doi.org/10.1142/s0219199722500626">10.1142/s0219199722500626</a>},
    number={10}, journal={Communications in Contemporary Mathematics}, publisher={World
    Scientific Pub Co Pte Ltd}, author={Winkler, Michael}, year={2022} }'
  chicago: Winkler, Michael. “Arbitrarily Fast Grow-up Rates in Quasilinear Keller–Segel
    Systems.” <i>Communications in Contemporary Mathematics</i> 25, no. 10 (2022).
    <a href="https://doi.org/10.1142/s0219199722500626">https://doi.org/10.1142/s0219199722500626</a>.
  ieee: 'M. Winkler, “Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems,”
    <i>Communications in Contemporary Mathematics</i>, vol. 25, no. 10, 2022, doi:
    <a href="https://doi.org/10.1142/s0219199722500626">10.1142/s0219199722500626</a>.'
  mla: Winkler, Michael. “Arbitrarily Fast Grow-up Rates in Quasilinear Keller–Segel
    Systems.” <i>Communications in Contemporary Mathematics</i>, vol. 25, no. 10,
    World Scientific Pub Co Pte Ltd, 2022, doi:<a href="https://doi.org/10.1142/s0219199722500626">10.1142/s0219199722500626</a>.
  short: M. Winkler, Communications in Contemporary Mathematics 25 (2022).
date_created: 2024-04-07T12:35:09Z
date_updated: 2024-04-07T12:35:53Z
doi: 10.1142/s0219199722500626
intvolume: '        25'
issue: '10'
keyword:
- Applied Mathematics
- General Mathematics
language:
- iso: eng
publication: Communications in Contemporary Mathematics
publication_identifier:
  issn:
  - 0219-1997
  - 1793-6683
publication_status: published
publisher: World Scientific Pub Co Pte Ltd
status: public
title: Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems
type: journal_article
user_id: '31496'
volume: 25
year: '2022'
...
---
_id: '53323'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title><jats:p>In a ball <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\Omega
    =B_R(0)\\subset \\mathbb {R}^n$$</jats:tex-math><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:msub>\r\n                    <mml:mi>B</mml:mi>\r\n                    <mml:mi>R</mml:mi>\r\n
    \                 </mml:msub>\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:mrow>\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></jats:alternatives></jats:inline-formula>,
    <jats:inline-formula><jats:alternatives><jats:tex-math>$$n\\ge 2$$</jats:tex-math><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>2</mml:mn>\r\n                </mml:mrow>\r\n              </mml:math></jats:alternatives></jats:inline-formula>,
    the chemotaxis system <jats:disp-formula><jats:alternatives><jats:tex-math>$$\\begin{aligned}
    \\left\\{ \\begin{array}{l}u_t = \\nabla \\cdot \\big ( D(u) \\nabla u \\big )
    - \\nabla \\cdot \\big ( uS(u)\\nabla v\\big ), \\\\ 0 = \\Delta v - \\mu + u,
    \\qquad \\mu =\\frac{1}{|\\Omega |} \\int _\\Omega u, \\end{array} \\right. \\qquad
    \\qquad (\\star ) \\end{aligned}$$</jats:tex-math><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: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:mi>t</mml:mi>\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:mrow>\r\n                                      <mml:mi>D</mml:mi>\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:mrow>\r\n                                      <mml:mi>∇</mml:mi>\r\n
    \                                     <mml:mi>u</mml:mi>\r\n                                      <mml:mrow>\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:mrow>\r\n
    \                                       <mml:mo>(</mml:mo>\r\n                                      </mml:mrow>\r\n
    \                                     <mml:mi>u</mml:mi>\r\n                                      <mml:mi>S</mml:mi>\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:mrow>\r\n                                      <mml:mi>∇</mml:mi>\r\n
    \                                     <mml:mi>v</mml:mi>\r\n                                      <mml:mrow>\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:mn>0</mml:mn>\r\n                                      <mml:mo>=</mml:mo>\r\n
    \                                     <mml:mi>Δ</mml:mi>\r\n                                      <mml:mi>v</mml:mi>\r\n
    \                                     <mml:mo>-</mml:mo>\r\n                                      <mml:mi>μ</mml:mi>\r\n
    \                                     <mml:mo>+</mml:mo>\r\n                                      <mml:mi>u</mml:mi>\r\n
    \                                     <mml:mo>,</mml:mo>\r\n                                      <mml:mspace
    />\r\n                                      <mml:mi>μ</mml:mi>\r\n                                      <mml:mo>=</mml:mo>\r\n
    \                                     <mml:mfrac>\r\n                                        <mml:mn>1</mml:mn>\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:mfrac>\r\n
    \                                     <mml:msub>\r\n                                        <mml:mo>∫</mml:mo>\r\n
    \                                       <mml:mi>Ω</mml:mi>\r\n                                      </mml:msub>\r\n
    \                                     <mml:mi>u</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:mfenced>\r\n
    \                         <mml:mspace />\r\n                          <mml:mspace
    />\r\n                          <mml:mrow>\r\n                            <mml:mo>(</mml:mo>\r\n
    \                           <mml:mo>⋆</mml:mo>\r\n                            <mml:mo>)</mml:mo>\r\n
    \                         </mml:mrow>\r\n                        </mml:mrow>\r\n
    \                     </mml:mtd>\r\n                    </mml:mtr>\r\n                  </mml:mtable>\r\n
    \               </mml:mrow>\r\n              </mml:math></jats:alternatives></jats:disp-formula>is
    considered under no-flux boundary conditions, with a focus on nonlinearities <jats:inline-formula><jats:alternatives><jats:tex-math>$$S\\in
    C^2([0,\\infty ))$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \               <mml:mrow>\r\n                  <mml:mi>S</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></jats:alternatives></jats:inline-formula>
    which exhibit super-algebraically fast decay in the sense that with some <jats:inline-formula><jats:alternatives><jats:tex-math>$$K_S&gt;0,
    \\beta \\in [0,1)$$</jats:tex-math><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>S</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:mi>β</mml:mi>\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:mn>1</mml:mn>\r\n
    \                   <mml:mo>)</mml:mo>\r\n                  </mml:mrow>\r\n                </mml:mrow>\r\n
    \             </mml:math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\xi
    _0&gt;0$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \               <mml:mrow>\r\n                  <mml:msub>\r\n                    <mml:mi>ξ</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></jats:alternatives></jats:inline-formula>,
    <jats:disp-formula><jats:alternatives><jats:tex-math>$$\\begin{aligned} S(\\xi
    )&gt;0 \\quad \\text{ and } \\quad S'(\\xi ) \\le -K_S\\xi ^{-\\beta } S(\\xi
    ) \\qquad \\text{ for } \\text{ all } \\xi \\ge \\xi _0. \\end{aligned}$$</jats:tex-math><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>S</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>&gt;</mml:mo>\r\n
    \                         <mml:mn>0</mml:mn>\r\n                          <mml:mspace
    />\r\n                          <mml:mspace />\r\n                          <mml:mtext>and</mml:mtext>\r\n
    \                         <mml:mspace />\r\n                          <mml:mspace
    />\r\n                          <mml:msup>\r\n                            <mml:mi>S</mml:mi>\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:mrow>\r\n                          <mml:mo>≤</mml:mo>\r\n
    \                         <mml:mo>-</mml:mo>\r\n                          <mml:msub>\r\n
    \                           <mml:mi>K</mml:mi>\r\n                            <mml:mi>S</mml:mi>\r\n
    \                         </mml:msub>\r\n                          <mml:msup>\r\n
    \                           <mml:mi>ξ</mml:mi>\r\n                            <mml:mrow>\r\n
    \                             <mml:mo>-</mml:mo>\r\n                              <mml:mi>β</mml:mi>\r\n
    \                           </mml:mrow>\r\n                          </mml:msup>\r\n
    \                         <mml:mi>S</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: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>ξ</mml:mi>\r\n
    \                         <mml:mo>≥</mml:mo>\r\n                          <mml:msub>\r\n
    \                           <mml:mi>ξ</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:mtd>\r\n                    </mml:mtr>\r\n
    \                 </mml:mtable>\r\n                </mml:mrow>\r\n              </mml:math></jats:alternatives></jats:disp-formula>It
    is, inter alia, shown that if furthermore <jats:inline-formula><jats:alternatives><jats:tex-math>$$D\\in
    C^2((0,\\infty ))$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \               <mml:mrow>\r\n                  <mml:mi>D</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></jats:alternatives></jats:inline-formula>
    is positive and suitably small in relation to <jats:italic>S</jats:italic> by
    satisfying <jats:disp-formula><jats:alternatives><jats:tex-math>$$\\begin{aligned}
    \\frac{\\xi S(\\xi )}{D(\\xi )} \\ge K_{SD}\\xi ^\\lambda \\qquad \\text{ for
    } \\text{ all } \\xi \\ge \\xi _0 \\end{aligned}$$</jats:tex-math><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:mfrac>\r\n
    \                           <mml:mrow>\r\n                              <mml:mi>ξ</mml:mi>\r\n
    \                             <mml:mi>S</mml:mi>\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:mrow>\r\n
    \                             <mml:mi>D</mml:mi>\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:mfrac>\r\n
    \                         <mml:mo>≥</mml:mo>\r\n                          <mml:msub>\r\n
    \                           <mml:mi>K</mml:mi>\r\n                            <mml:mrow>\r\n
    \                             <mml:mi>SD</mml:mi>\r\n                            </mml:mrow>\r\n
    \                         </mml:msub>\r\n                          <mml:msup>\r\n
    \                           <mml:mi>ξ</mml:mi>\r\n                            <mml:mi>λ</mml:mi>\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>ξ</mml:mi>\r\n                          <mml:mo>≥</mml:mo>\r\n
    \                         <mml:msub>\r\n                            <mml:mi>ξ</mml:mi>\r\n
    \                           <mml:mn>0</mml:mn>\r\n                          </mml:msub>\r\n
    \                       </mml:mrow>\r\n                      </mml:mtd>\r\n                    </mml:mtr>\r\n
    \                 </mml:mtable>\r\n                </mml:mrow>\r\n              </mml:math></jats:alternatives></jats:disp-formula>with
    some <jats:inline-formula><jats:alternatives><jats:tex-math>$$K_{SD}&gt;0$$</jats:tex-math><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:mrow>\r\n
    \                     <mml:mi>SD</mml:mi>\r\n                    </mml:mrow>\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></jats:alternatives></jats:inline-formula>
    and <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\lambda &gt;\\frac{2}{n}$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                <mml:mrow>\r\n
    \                 <mml:mi>λ</mml:mi>\r\n                  <mml:mo>&gt;</mml:mo>\r\n
    \                 <mml:mfrac>\r\n                    <mml:mn>2</mml:mn>\r\n                    <mml:mi>n</mml:mi>\r\n
    \                 </mml:mfrac>\r\n                </mml:mrow>\r\n              </mml:math></jats:alternatives></jats:inline-formula>,
    then throughout a considerably large set of initial data, (<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\star
    $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \               <mml:mo>⋆</mml:mo>\r\n              </mml:math></jats:alternatives></jats:inline-formula>)
    admits global classical solutions (<jats:italic>u</jats:italic>, <jats:italic>v</jats:italic>)
    fulfilling <jats:disp-formula><jats:alternatives><jats:tex-math>$$\\begin{aligned}
    \\frac{z(t)}{C} \\le \\Vert u(\\cdot ,t)\\Vert _{L^\\infty (\\Omega )} \\le Cz(t)
    \\qquad \\text{ for } \\text{ all } t&gt;0, \\end{aligned}$$</jats:tex-math><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:mfrac>\r\n
    \                           <mml:mrow>\r\n                              <mml:mi>z</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:mi>C</mml:mi>\r\n                          </mml:mfrac>\r\n
    \                         <mml:mo>≤</mml:mo>\r\n                          <mml:msub>\r\n
    \                           <mml:mrow>\r\n                              <mml:mo>‖</mml:mo>\r\n
    \                             <mml:mi>u</mml:mi>\r\n                              <mml:mrow>\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:mrow>\r\n
    \                             <mml:mo>‖</mml:mo>\r\n                            </mml:mrow>\r\n
    \                           <mml:mrow>\r\n                              <mml:msup>\r\n
    \                               <mml:mi>L</mml:mi>\r\n                                <mml:mi>∞</mml:mi>\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:msub>\r\n
    \                         <mml:mo>≤</mml:mo>\r\n                          <mml:mi>C</mml:mi>\r\n
    \                         <mml:mi>z</mml:mi>\r\n                          <mml:mrow>\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>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></jats:alternatives></jats:disp-formula>with
    some <jats:inline-formula><jats:alternatives><jats:tex-math>$$C=C^{(u,v)}\\ge
    1$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \               <mml:mrow>\r\n                  <mml:mi>C</mml:mi>\r\n                  <mml:mo>=</mml:mo>\r\n
    \                 <mml:msup>\r\n                    <mml:mi>C</mml:mi>\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:mi>v</mml:mi>\r\n
    \                     <mml:mo>)</mml:mo>\r\n                    </mml:mrow>\r\n
    \                 </mml:msup>\r\n                  <mml:mo>≥</mml:mo>\r\n                  <mml:mn>1</mml:mn>\r\n
    \               </mml:mrow>\r\n              </mml:math></jats:alternatives></jats:inline-formula>,
    where <jats:italic>z</jats:italic> denotes the solution of <jats:disp-formula><jats:alternatives><jats:tex-math>$$\\begin{aligned}
    \\left\\{ \\begin{array}{l}z'(t) = z^2(t) \\cdot S\\big ( z(t)\\big ), \\qquad
    t&gt;0, \\\\ z(0)=\\xi _0, \\end{array} \\right. \\end{aligned}$$</jats:tex-math><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:msup>\r\n                                      <mml:mi>z</mml:mi>\r\n
    \                                     <mml:mo>′</mml:mo>\r\n                                    </mml:msup>\r\n
    \                                   <mml:mrow>\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:mo>=</mml:mo>\r\n
    \                                   <mml:msup>\r\n                                      <mml:mi>z</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>t</mml:mi>\r\n                                      <mml:mo>)</mml:mo>\r\n
    \                                   </mml:mrow>\r\n                                    <mml:mo>·</mml:mo>\r\n
    \                                   <mml:mi>S</mml:mi>\r\n                                    <mml:mrow>\r\n
    \                                     <mml:mo>(</mml:mo>\r\n                                    </mml:mrow>\r\n
    \                                   <mml:mi>z</mml:mi>\r\n                                    <mml:mrow>\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:mrow>\r\n                                      <mml:mo>)</mml:mo>\r\n
    \                                   </mml:mrow>\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:mi>z</mml:mi>\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:mrow>\r\n
    \                                   <mml:mo>=</mml:mo>\r\n                                    <mml:msub>\r\n
    \                                     <mml:mi>ξ</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: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></jats:alternatives></jats:disp-formula>which
    is seen to exist globally, and to satisfy <jats:inline-formula><jats:alternatives><jats:tex-math>$$z(t)\\rightarrow
    +\\infty $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \               <mml:mrow>\r\n                  <mml:mi>z</mml:mi>\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:mo>+</mml:mo>\r\n
    \                 <mml:mi>∞</mml:mi>\r\n                </mml:mrow>\r\n              </mml:math></jats:alternatives></jats:inline-formula>
    as <jats:inline-formula><jats:alternatives><jats:tex-math>$$t\\rightarrow \\infty
    $$</jats:tex-math><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:mi>∞</mml:mi>\r\n                </mml:mrow>\r\n              </mml:math></jats:alternatives></jats:inline-formula>.
    As particular examples, exponentially and doubly exponentially decaying <jats:italic>S</jats:italic>
    are found to imply corresponding infinite-time blow-up properties in (<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\star
    $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \               <mml:mo>⋆</mml:mo>\r\n              </mml:math></jats:alternatives></jats:inline-formula>)
    at logarithmic and doubly logarithmic rates, respectively.</jats:p>"
author:
- first_name: Michael
  full_name: Winkler, Michael
  last_name: Winkler
citation:
  ama: Winkler M. Slow Grow-up in a Quasilinear Keller–Segel System. <i>Journal of
    Dynamics and Differential Equations</i>. Published online 2022. doi:<a href="https://doi.org/10.1007/s10884-022-10167-w">10.1007/s10884-022-10167-w</a>
  apa: Winkler, M. (2022). Slow Grow-up in a Quasilinear Keller–Segel System. <i>Journal
    of Dynamics and Differential Equations</i>. <a href="https://doi.org/10.1007/s10884-022-10167-w">https://doi.org/10.1007/s10884-022-10167-w</a>
  bibtex: '@article{Winkler_2022, title={Slow Grow-up in a Quasilinear Keller–Segel
    System}, DOI={<a href="https://doi.org/10.1007/s10884-022-10167-w">10.1007/s10884-022-10167-w</a>},
    journal={Journal of Dynamics and Differential Equations}, publisher={Springer
    Science and Business Media LLC}, author={Winkler, Michael}, year={2022} }'
  chicago: Winkler, Michael. “Slow Grow-up in a Quasilinear Keller–Segel System.”
    <i>Journal of Dynamics and Differential Equations</i>, 2022. <a href="https://doi.org/10.1007/s10884-022-10167-w">https://doi.org/10.1007/s10884-022-10167-w</a>.
  ieee: 'M. Winkler, “Slow Grow-up in a Quasilinear Keller–Segel System,” <i>Journal
    of Dynamics and Differential Equations</i>, 2022, doi: <a href="https://doi.org/10.1007/s10884-022-10167-w">10.1007/s10884-022-10167-w</a>.'
  mla: Winkler, Michael. “Slow Grow-up in a Quasilinear Keller–Segel System.” <i>Journal
    of Dynamics and Differential Equations</i>, Springer Science and Business Media
    LLC, 2022, doi:<a href="https://doi.org/10.1007/s10884-022-10167-w">10.1007/s10884-022-10167-w</a>.
  short: M. Winkler, Journal of Dynamics and Differential Equations (2022).
date_created: 2024-04-07T12:39:12Z
date_updated: 2024-04-07T12:39:17Z
doi: 10.1007/s10884-022-10167-w
keyword:
- Analysis
language:
- iso: eng
publication: Journal of Dynamics and Differential Equations
publication_identifier:
  issn:
  - 1040-7294
  - 1572-9222
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Slow Grow-up in a Quasilinear Keller–Segel System
type: journal_article
user_id: '31496'
year: '2022'
...
---
_id: '53327'
author:
- first_name: Youshan
  full_name: Tao, Youshan
  last_name: Tao
- first_name: Michael
  full_name: Winkler, Michael
  last_name: Winkler
citation:
  ama: Tao Y, Winkler M. Global solutions to a Keller-Segel-consumption system involving
    singularly signal-dependent motilities in domains of arbitrary dimension. <i>Journal
    of Differential Equations</i>. 2022;343:390-418. doi:<a href="https://doi.org/10.1016/j.jde.2022.10.022">10.1016/j.jde.2022.10.022</a>
  apa: Tao, Y., &#38; Winkler, M. (2022). Global solutions to a Keller-Segel-consumption
    system involving singularly signal-dependent motilities in domains of arbitrary
    dimension. <i>Journal of Differential Equations</i>, <i>343</i>, 390–418. <a href="https://doi.org/10.1016/j.jde.2022.10.022">https://doi.org/10.1016/j.jde.2022.10.022</a>
  bibtex: '@article{Tao_Winkler_2022, title={Global solutions to a Keller-Segel-consumption
    system involving singularly signal-dependent motilities in domains of arbitrary
    dimension}, volume={343}, DOI={<a href="https://doi.org/10.1016/j.jde.2022.10.022">10.1016/j.jde.2022.10.022</a>},
    journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Tao,
    Youshan and Winkler, Michael}, year={2022}, pages={390–418} }'
  chicago: 'Tao, Youshan, and Michael Winkler. “Global Solutions to a Keller-Segel-Consumption
    System Involving Singularly Signal-Dependent Motilities in Domains of Arbitrary
    Dimension.” <i>Journal of Differential Equations</i> 343 (2022): 390–418. <a href="https://doi.org/10.1016/j.jde.2022.10.022">https://doi.org/10.1016/j.jde.2022.10.022</a>.'
  ieee: 'Y. Tao and M. Winkler, “Global solutions to a Keller-Segel-consumption system
    involving singularly signal-dependent motilities in domains of arbitrary dimension,”
    <i>Journal of Differential Equations</i>, vol. 343, pp. 390–418, 2022, doi: <a
    href="https://doi.org/10.1016/j.jde.2022.10.022">10.1016/j.jde.2022.10.022</a>.'
  mla: Tao, Youshan, and Michael Winkler. “Global Solutions to a Keller-Segel-Consumption
    System Involving Singularly Signal-Dependent Motilities in Domains of Arbitrary
    Dimension.” <i>Journal of Differential Equations</i>, vol. 343, Elsevier BV, 2022,
    pp. 390–418, doi:<a href="https://doi.org/10.1016/j.jde.2022.10.022">10.1016/j.jde.2022.10.022</a>.
  short: Y. Tao, M. Winkler, Journal of Differential Equations 343 (2022) 390–418.
date_created: 2024-04-07T12:42:28Z
date_updated: 2024-04-07T12:42:32Z
doi: 10.1016/j.jde.2022.10.022
intvolume: '       343'
keyword:
- Analysis
- Applied Mathematics
language:
- iso: eng
page: 390-418
publication: Journal of Differential Equations
publication_identifier:
  issn:
  - 0022-0396
publication_status: published
publisher: Elsevier BV
status: public
title: Global solutions to a Keller-Segel-consumption system involving singularly
  signal-dependent motilities in domains of arbitrary dimension
type: journal_article
user_id: '31496'
volume: 343
year: '2022'
...
---
_id: '53325'
article_number: '113153'
author:
- first_name: Laurent
  full_name: Desvillettes, Laurent
  last_name: Desvillettes
- first_name: Philippe
  full_name: Laurençot, Philippe
  last_name: Laurençot
- first_name: Ariane
  full_name: Trescases, Ariane
  last_name: Trescases
- first_name: Michael
  full_name: Winkler, Michael
  last_name: Winkler
citation:
  ama: Desvillettes L, Laurençot P, Trescases A, Winkler M. Weak solutions to triangular
    cross diffusion systems modeling chemotaxis with local sensing. <i>Nonlinear Analysis</i>.
    2022;226. doi:<a href="https://doi.org/10.1016/j.na.2022.113153">10.1016/j.na.2022.113153</a>
  apa: Desvillettes, L., Laurençot, P., Trescases, A., &#38; Winkler, M. (2022). Weak
    solutions to triangular cross diffusion systems modeling chemotaxis with local
    sensing. <i>Nonlinear Analysis</i>, <i>226</i>, Article 113153. <a href="https://doi.org/10.1016/j.na.2022.113153">https://doi.org/10.1016/j.na.2022.113153</a>
  bibtex: '@article{Desvillettes_Laurençot_Trescases_Winkler_2022, title={Weak solutions
    to triangular cross diffusion systems modeling chemotaxis with local sensing},
    volume={226}, DOI={<a href="https://doi.org/10.1016/j.na.2022.113153">10.1016/j.na.2022.113153</a>},
    number={113153}, journal={Nonlinear Analysis}, publisher={Elsevier BV}, author={Desvillettes,
    Laurent and Laurençot, Philippe and Trescases, Ariane and Winkler, Michael}, year={2022}
    }'
  chicago: Desvillettes, Laurent, Philippe Laurençot, Ariane Trescases, and Michael
    Winkler. “Weak Solutions to Triangular Cross Diffusion Systems Modeling Chemotaxis
    with Local Sensing.” <i>Nonlinear Analysis</i> 226 (2022). <a href="https://doi.org/10.1016/j.na.2022.113153">https://doi.org/10.1016/j.na.2022.113153</a>.
  ieee: 'L. Desvillettes, P. Laurençot, A. Trescases, and M. Winkler, “Weak solutions
    to triangular cross diffusion systems modeling chemotaxis with local sensing,”
    <i>Nonlinear Analysis</i>, vol. 226, Art. no. 113153, 2022, doi: <a href="https://doi.org/10.1016/j.na.2022.113153">10.1016/j.na.2022.113153</a>.'
  mla: Desvillettes, Laurent, et al. “Weak Solutions to Triangular Cross Diffusion
    Systems Modeling Chemotaxis with Local Sensing.” <i>Nonlinear Analysis</i>, vol.
    226, 113153, Elsevier BV, 2022, doi:<a href="https://doi.org/10.1016/j.na.2022.113153">10.1016/j.na.2022.113153</a>.
  short: L. Desvillettes, P. Laurençot, A. Trescases, M. Winkler, Nonlinear Analysis
    226 (2022).
date_created: 2024-04-07T12:41:15Z
date_updated: 2024-04-07T12:41:20Z
doi: 10.1016/j.na.2022.113153
intvolume: '       226'
keyword:
- Applied Mathematics
- Analysis
language:
- iso: eng
publication: Nonlinear Analysis
publication_identifier:
  issn:
  - 0362-546X
publication_status: published
publisher: Elsevier BV
status: public
title: Weak solutions to triangular cross diffusion systems modeling chemotaxis with
  local sensing
type: journal_article
user_id: '31496'
volume: 226
year: '2022'
...
---
_id: '53331'
abstract:
- lang: eng
  text: "<jats:p>In a ball <jats:inline-formula><jats:alternatives><jats:tex-math>$\\Omega
    \\subset \\mathbb {R}^{n}$</jats:tex-math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\"
    mime-subtype=\"png\" xlink:href=\"S0308210522000397_inline1.png\" /></jats:alternatives></jats:inline-formula>
    with <jats:inline-formula><jats:alternatives><jats:tex-math>$n\\ge 2$</jats:tex-math><jats:inline-graphic
    xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0308210522000397_inline2.png\"
    /></jats:alternatives></jats:inline-formula>, the chemotaxis system\r\n<jats:disp-formula><jats:alternatives><jats:tex-math>\\[
    \\left\\{ \\begin{array}{@{}l} u_t = \\nabla \\cdot \\big( D(u)\\nabla u\\big)
    + \\nabla\\cdot \\big(\\dfrac{u}{v} \\nabla v\\big), \\\\ 0=\\Delta v - uv \\end{array}
    \\right. \\]</jats:tex-math><jats:graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\"
    mime-subtype=\"png\" mimetype=\"image\" position=\"float\" xlink:href=\"S0308210522000397_eqnU1.png\"
    /></jats:alternatives></jats:disp-formula>is considered along with no-flux boundary
    conditions for <jats:inline-formula><jats:alternatives><jats:tex-math>$u$</jats:tex-math><jats:inline-graphic
    xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0308210522000397_inline3.png\"
    /></jats:alternatives></jats:inline-formula> and with prescribed constant positive
    Dirichlet boundary data for <jats:inline-formula><jats:alternatives><jats:tex-math>$v$</jats:tex-math><jats:inline-graphic
    xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0308210522000397_inline4.png\"
    /></jats:alternatives></jats:inline-formula>. It is shown that if <jats:inline-formula><jats:alternatives><jats:tex-math>$D\\in
    C^{3}([0,\\infty ))$</jats:tex-math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\"
    mime-subtype=\"png\" xlink:href=\"S0308210522000397_inline5.png\" /></jats:alternatives></jats:inline-formula>
    is such that <jats:inline-formula><jats:alternatives><jats:tex-math>$0&lt; D(\\xi
    ) \\le {K_D} (\\xi +1)^{-\\alpha }$</jats:tex-math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\"
    mime-subtype=\"png\" xlink:href=\"S0308210522000397_inline6.png\" /></jats:alternatives></jats:inline-formula>
    for all <jats:inline-formula><jats:alternatives><jats:tex-math>$\\xi &gt;0$</jats:tex-math><jats:inline-graphic
    xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0308210522000397_inline7.png\"
    /></jats:alternatives></jats:inline-formula> with some <jats:inline-formula><jats:alternatives><jats:tex-math>${K_D}&gt;0$</jats:tex-math><jats:inline-graphic
    xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0308210522000397_inline8.png\"
    /></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$\\alpha
    &gt;0$</jats:tex-math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\"
    mime-subtype=\"png\" xlink:href=\"S0308210522000397_inline9.png\" /></jats:alternatives></jats:inline-formula>,
    then for all initial data from a considerably large set of radial functions on
    <jats:inline-formula><jats:alternatives><jats:tex-math>$\\Omega$</jats:tex-math><jats:inline-graphic
    xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0308210522000397_inline10.png\"
    /></jats:alternatives></jats:inline-formula>, the corresponding initial-boundary
    value problem admits a solution blowing up in finite time.</jats:p>"
author:
- first_name: Yulan
  full_name: Wang, Yulan
  last_name: Wang
- first_name: Michael
  full_name: Winkler, Michael
  last_name: Winkler
citation:
  ama: 'Wang Y, Winkler M. Finite-time blow-up in a repulsive chemotaxis-consumption
    system. <i>Proceedings of the Royal Society of Edinburgh: Section A Mathematics</i>.
    2022;153(4):1150-1166. doi:<a href="https://doi.org/10.1017/prm.2022.39">10.1017/prm.2022.39</a>'
  apa: 'Wang, Y., &#38; Winkler, M. (2022). Finite-time blow-up in a repulsive chemotaxis-consumption
    system. <i>Proceedings of the Royal Society of Edinburgh: Section A Mathematics</i>,
    <i>153</i>(4), 1150–1166. <a href="https://doi.org/10.1017/prm.2022.39">https://doi.org/10.1017/prm.2022.39</a>'
  bibtex: '@article{Wang_Winkler_2022, title={Finite-time blow-up in a repulsive chemotaxis-consumption
    system}, volume={153}, DOI={<a href="https://doi.org/10.1017/prm.2022.39">10.1017/prm.2022.39</a>},
    number={4}, journal={Proceedings of the Royal Society of Edinburgh: Section A
    Mathematics}, publisher={Cambridge University Press (CUP)}, author={Wang, Yulan
    and Winkler, Michael}, year={2022}, pages={1150–1166} }'
  chicago: 'Wang, Yulan, and Michael Winkler. “Finite-Time Blow-up in a Repulsive
    Chemotaxis-Consumption System.” <i>Proceedings of the Royal Society of Edinburgh:
    Section A Mathematics</i> 153, no. 4 (2022): 1150–66. <a href="https://doi.org/10.1017/prm.2022.39">https://doi.org/10.1017/prm.2022.39</a>.'
  ieee: 'Y. Wang and M. Winkler, “Finite-time blow-up in a repulsive chemotaxis-consumption
    system,” <i>Proceedings of the Royal Society of Edinburgh: Section A Mathematics</i>,
    vol. 153, no. 4, pp. 1150–1166, 2022, doi: <a href="https://doi.org/10.1017/prm.2022.39">10.1017/prm.2022.39</a>.'
  mla: 'Wang, Yulan, and Michael Winkler. “Finite-Time Blow-up in a Repulsive Chemotaxis-Consumption
    System.” <i>Proceedings of the Royal Society of Edinburgh: Section A Mathematics</i>,
    vol. 153, no. 4, Cambridge University Press (CUP), 2022, pp. 1150–66, doi:<a href="https://doi.org/10.1017/prm.2022.39">10.1017/prm.2022.39</a>.'
  short: 'Y. Wang, M. Winkler, Proceedings of the Royal Society of Edinburgh: Section
    A Mathematics 153 (2022) 1150–1166.'
date_created: 2024-04-07T12:44:26Z
date_updated: 2024-04-07T12:44:30Z
doi: 10.1017/prm.2022.39
intvolume: '       153'
issue: '4'
keyword:
- General Mathematics
language:
- iso: eng
page: 1150-1166
publication: 'Proceedings of the Royal Society of Edinburgh: Section A Mathematics'
publication_identifier:
  issn:
  - 0308-2105
  - 1473-7124
publication_status: published
publisher: Cambridge University Press (CUP)
status: public
title: Finite-time blow-up in a repulsive chemotaxis-consumption system
type: journal_article
user_id: '31496'
volume: 153
year: '2022'
...
---
_id: '53344'
abstract:
- lang: eng
  text: '<jats:p> A no-flux initial-boundary value problem for the cross-diffusion
    system [Formula: see text] is considered in smoothly bounded domains [Formula:
    see text] with [Formula: see text]. It is shown that whenever [Formula: see text]
    is positive on [Formula: see text] and such that [Formula: see text] for some
    [Formula: see text], for all suitably regular positive initial data a global very
    weak solution, particularly preserving mass in its first component, can be constructed.
    This extends previous results which either concentrate on non-degenerate analogs,
    or are restricted to the special case [Formula: see text]. </jats:p><jats:p> To
    appropriately cope with the considerably stronger cross-degeneracies thus allowed
    through [Formula: see text] when [Formula: see text] is large, in its core part
    the analysis relies on the use of the Moser–Trudinger inequality in controlling
    the respective diffusion rates [Formula: see text] from below. </jats:p>'
author:
- first_name: Michael
  full_name: Winkler, Michael
  last_name: Winkler
citation:
  ama: Winkler M. Application of the Moser–Trudinger inequality in the construction
    of global solutions to a strongly degenerate migration model. <i>Bulletin of Mathematical
    Sciences</i>. 2022;13(02). doi:<a href="https://doi.org/10.1142/s1664360722500126">10.1142/s1664360722500126</a>
  apa: Winkler, M. (2022). Application of the Moser–Trudinger inequality in the construction
    of global solutions to a strongly degenerate migration model. <i>Bulletin of Mathematical
    Sciences</i>, <i>13</i>(02). <a href="https://doi.org/10.1142/s1664360722500126">https://doi.org/10.1142/s1664360722500126</a>
  bibtex: '@article{Winkler_2022, title={Application of the Moser–Trudinger inequality
    in the construction of global solutions to a strongly degenerate migration model},
    volume={13}, DOI={<a href="https://doi.org/10.1142/s1664360722500126">10.1142/s1664360722500126</a>},
    number={02}, journal={Bulletin of Mathematical Sciences}, publisher={World Scientific
    Pub Co Pte Ltd}, author={Winkler, Michael}, year={2022} }'
  chicago: Winkler, Michael. “Application of the Moser–Trudinger Inequality in the
    Construction of Global Solutions to a Strongly Degenerate Migration Model.” <i>Bulletin
    of Mathematical Sciences</i> 13, no. 02 (2022). <a href="https://doi.org/10.1142/s1664360722500126">https://doi.org/10.1142/s1664360722500126</a>.
  ieee: 'M. Winkler, “Application of the Moser–Trudinger inequality in the construction
    of global solutions to a strongly degenerate migration model,” <i>Bulletin of
    Mathematical Sciences</i>, vol. 13, no. 02, 2022, doi: <a href="https://doi.org/10.1142/s1664360722500126">10.1142/s1664360722500126</a>.'
  mla: Winkler, Michael. “Application of the Moser–Trudinger Inequality in the Construction
    of Global Solutions to a Strongly Degenerate Migration Model.” <i>Bulletin of
    Mathematical Sciences</i>, vol. 13, no. 02, World Scientific Pub Co Pte Ltd, 2022,
    doi:<a href="https://doi.org/10.1142/s1664360722500126">10.1142/s1664360722500126</a>.
  short: M. Winkler, Bulletin of Mathematical Sciences 13 (2022).
date_created: 2024-04-07T12:55:07Z
date_updated: 2024-04-07T12:55:11Z
doi: 10.1142/s1664360722500126
intvolume: '        13'
issue: '02'
keyword:
- General Mathematics
language:
- iso: eng
publication: Bulletin of Mathematical Sciences
publication_identifier:
  issn:
  - 1664-3607
  - 1664-3615
publication_status: published
publisher: World Scientific Pub Co Pte Ltd
status: public
title: Application of the Moser–Trudinger inequality in the construction of global
  solutions to a strongly degenerate migration model
type: journal_article
user_id: '31496'
volume: 13
year: '2022'
...
---
_id: '35788'
author:
- first_name: Martin
  full_name: Fochmann, Martin
  last_name: Fochmann
- first_name: Vanessa
  full_name: Heinemann-Heile, Vanessa
  id: '83380'
  last_name: Heinemann-Heile
- first_name: Hans-Peter
  full_name: Huber, Hans-Peter
  last_name: Huber
- first_name: Ralf
  full_name: Maiterth, Ralf
  last_name: Maiterth
- first_name: Caren
  full_name: Sureth-Sloane, Caren
  id: '530'
  last_name: Sureth-Sloane
  orcid: ' 0000-0002-8183-5901'
citation:
  ama: Fochmann M, Heinemann-Heile V, Huber H-P, Maiterth R, Sureth-Sloane C. <i>Zusatzkosten
    der Besteuerung – Eine Analyse des steuerlichen Verwaltungsaufwands und der subjektiv
    wahrgenommenen Steuerbelastung (An Empirical Analysis of Firms’ Hidden Cost of
    Taxation)</i>. Vol 100.; 2022. doi:<a href="https://doi.org/10.2139/ssrn.4210460">10.2139/ssrn.4210460</a>
  apa: Fochmann, M., Heinemann-Heile, V., Huber, H.-P., Maiterth, R., &#38; Sureth-Sloane,
    C. (2022). <i>Zusatzkosten der Besteuerung – Eine Analyse des steuerlichen Verwaltungsaufwands
    und der subjektiv wahrgenommenen Steuerbelastung (An Empirical Analysis of Firms’
    Hidden Cost of Taxation)</i> (Vol. 100). <a href="https://doi.org/10.2139/ssrn.4210460">https://doi.org/10.2139/ssrn.4210460</a>
  bibtex: '@book{Fochmann_Heinemann-Heile_Huber_Maiterth_Sureth-Sloane_2022, series={TRR
    266 Accounting for Transparency Working Paper Series}, title={Zusatzkosten der
    Besteuerung – Eine Analyse des steuerlichen Verwaltungsaufwands und der subjektiv
    wahrgenommenen Steuerbelastung (An Empirical Analysis of Firms’ Hidden Cost of
    Taxation)}, volume={100}, DOI={<a href="https://doi.org/10.2139/ssrn.4210460">10.2139/ssrn.4210460</a>},
    author={Fochmann, Martin and Heinemann-Heile, Vanessa and Huber, Hans-Peter and
    Maiterth, Ralf and Sureth-Sloane, Caren}, year={2022}, collection={TRR 266 Accounting
    for Transparency Working Paper Series} }'
  chicago: Fochmann, Martin, Vanessa Heinemann-Heile, Hans-Peter Huber, Ralf Maiterth,
    and Caren Sureth-Sloane. <i>Zusatzkosten der Besteuerung – Eine Analyse des steuerlichen
    Verwaltungsaufwands und der subjektiv wahrgenommenen Steuerbelastung (An Empirical
    Analysis of Firms’ Hidden Cost of Taxation)</i>. Vol. 100. TRR 266 Accounting
    for Transparency Working Paper Series, 2022. <a href="https://doi.org/10.2139/ssrn.4210460">https://doi.org/10.2139/ssrn.4210460</a>.
  ieee: M. Fochmann, V. Heinemann-Heile, H.-P. Huber, R. Maiterth, and C. Sureth-Sloane,
    <i>Zusatzkosten der Besteuerung – Eine Analyse des steuerlichen Verwaltungsaufwands
    und der subjektiv wahrgenommenen Steuerbelastung (An Empirical Analysis of Firms’
    Hidden Cost of Taxation)</i>, vol. 100. 2022.
  mla: Fochmann, Martin, et al. <i>Zusatzkosten der Besteuerung – Eine Analyse des
    steuerlichen Verwaltungsaufwands und der subjektiv wahrgenommenen Steuerbelastung
    (An Empirical Analysis of Firms’ Hidden Cost of Taxation)</i>. 2022, doi:<a href="https://doi.org/10.2139/ssrn.4210460">10.2139/ssrn.4210460</a>.
  short: M. Fochmann, V. Heinemann-Heile, H.-P. Huber, R. Maiterth, C. Sureth-Sloane,
    Zusatzkosten der Besteuerung – Eine Analyse des steuerlichen Verwaltungsaufwands
    und der subjektiv wahrgenommenen Steuerbelastung (An Empirical Analysis of Firms’
    Hidden Cost of Taxation), 2022.
date_created: 2023-01-10T10:51:40Z
date_updated: 2024-04-08T11:33:02Z
department:
- _id: '187'
doi: 10.2139/ssrn.4210460
intvolume: '       100'
keyword:
- General Earth and Planetary Sciences
- General Environmental Science
language:
- iso: ger
main_file_link:
- open_access: '1'
oa: '1'
publication_identifier:
  issn:
  - 1556-5068
publication_status: published
series_title: TRR 266 Accounting for Transparency Working Paper Series
status: public
title: Zusatzkosten der Besteuerung – Eine Analyse des steuerlichen Verwaltungsaufwands
  und der subjektiv wahrgenommenen Steuerbelastung (An Empirical Analysis of Firms’
  Hidden Cost of Taxation)
type: working_paper
user_id: '530'
volume: 100
year: '2022'
...
---
_id: '35795'
author:
- first_name: Stefan
  full_name: Greil, Stefan
  last_name: Greil
- first_name: Michael
  full_name: Overesch, Michael
  last_name: Overesch
- first_name: Anna
  full_name: Rohlfing-Bastian, Anna
  last_name: Rohlfing-Bastian
- first_name: Ulrich
  full_name: Schreiber, Ulrich
  last_name: Schreiber
- first_name: Caren
  full_name: Sureth-Sloane, Caren
  id: '530'
  last_name: Sureth-Sloane
  orcid: ' 0000-0002-8183-5901'
citation:
  ama: Greil S, Overesch M, Rohlfing-Bastian A, Schreiber U, Sureth-Sloane C. <i>Towards
    an Amended Arm’s Length Principle - Tackling Complexity and Implementing Destination
    Rules in Transfer Pricing</i>. Vol 89.; 2022. doi:<a href="https://doi.org/10.2139/ssrn.4166972">10.2139/ssrn.4166972</a>
  apa: Greil, S., Overesch, M., Rohlfing-Bastian, A., Schreiber, U., &#38; Sureth-Sloane,
    C. (2022). <i>Towards an Amended Arm’s Length Principle - Tackling complexity
    and implementing destination rules in transfer pricing</i> (Vol. 89). <a href="https://doi.org/10.2139/ssrn.4166972">https://doi.org/10.2139/ssrn.4166972</a>
  bibtex: '@book{Greil_Overesch_Rohlfing-Bastian_Schreiber_Sureth-Sloane_2022, series={TRR
    266 Accounting for Transparency Working Paper Series}, title={Towards an Amended
    Arm’s Length Principle - Tackling complexity and implementing destination rules
    in transfer pricing}, volume={89}, DOI={<a href="https://doi.org/10.2139/ssrn.4166972">10.2139/ssrn.4166972</a>},
    author={Greil, Stefan and Overesch, Michael and Rohlfing-Bastian, Anna and Schreiber,
    Ulrich and Sureth-Sloane, Caren}, year={2022}, collection={TRR 266 Accounting
    for Transparency Working Paper Series} }'
  chicago: Greil, Stefan, Michael Overesch, Anna Rohlfing-Bastian, Ulrich Schreiber,
    and Caren Sureth-Sloane. <i>Towards an Amended Arm’s Length Principle - Tackling
    Complexity and Implementing Destination Rules in Transfer Pricing</i>. Vol. 89.
    TRR 266 Accounting for Transparency Working Paper Series, 2022. <a href="https://doi.org/10.2139/ssrn.4166972">https://doi.org/10.2139/ssrn.4166972</a>.
  ieee: S. Greil, M. Overesch, A. Rohlfing-Bastian, U. Schreiber, and C. Sureth-Sloane,
    <i>Towards an Amended Arm’s Length Principle - Tackling complexity and implementing
    destination rules in transfer pricing</i>, vol. 89. 2022.
  mla: Greil, Stefan, et al. <i>Towards an Amended Arm’s Length Principle - Tackling
    Complexity and Implementing Destination Rules in Transfer Pricing</i>. 2022, doi:<a
    href="https://doi.org/10.2139/ssrn.4166972">10.2139/ssrn.4166972</a>.
  short: S. Greil, M. Overesch, A. Rohlfing-Bastian, U. Schreiber, C. Sureth-Sloane,
    Towards an Amended Arm’s Length Principle - Tackling Complexity and Implementing
    Destination Rules in Transfer Pricing, 2022.
date_created: 2023-01-10T11:00:37Z
date_updated: 2024-04-08T11:32:32Z
department:
- _id: '187'
doi: 10.2139/ssrn.4166972
intvolume: '        89'
language:
- iso: eng
main_file_link:
- open_access: '1'
oa: '1'
publication_identifier:
  issn:
  - 1556-5068
publication_status: published
series_title: TRR 266 Accounting for Transparency Working Paper Series
status: public
title: Towards an Amended Arm's Length Principle - Tackling complexity and implementing
  destination rules in transfer pricing
type: working_paper
user_id: '530'
volume: 89
year: '2022'
...
---
_id: '52574'
author:
- first_name: Gerda
  full_name: Werth, Gerda
  id: '578'
  last_name: Werth
citation:
  ama: 'Werth G. Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde
    Vaertings. In: <i>Beiträge zum Mathematikunterricht</i>. WTM; 2022. doi:<a href="https://doi.org/10.37626/GA9783959872089.0">https://doi.org/10.37626/GA9783959872089.0</a>'
  apa: Werth, G. (2022). Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde
    Vaertings. <i>Beiträge zum Mathematikunterricht</i>. 56. Jahrestagung der Gesellschaft
    für Didaktik der Mathematik, Frankfurt am. Main. <a href="https://doi.org/10.37626/GA9783959872089.0">https://doi.org/10.37626/GA9783959872089.0</a>
  bibtex: '@inproceedings{Werth_2022, place={Münster}, title={Neue Wege im mathematischen
    Unterricht - Auf den Spuren Mathilde Vaertings}, DOI={<a href="https://doi.org/10.37626/GA9783959872089.0">https://doi.org/10.37626/GA9783959872089.0</a>},
    booktitle={Beiträge zum Mathematikunterricht}, publisher={WTM}, author={Werth,
    Gerda}, year={2022} }'
  chicago: 'Werth, Gerda. “Neue Wege im mathematischen Unterricht - Auf den Spuren
    Mathilde Vaertings.” In <i>Beiträge zum Mathematikunterricht</i>. Münster: WTM,
    2022. <a href="https://doi.org/10.37626/GA9783959872089.0">https://doi.org/10.37626/GA9783959872089.0</a>.'
  ieee: 'G. Werth, “Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde
    Vaertings,” presented at the 56. Jahrestagung der Gesellschaft für Didaktik der
    Mathematik, Frankfurt am. Main, 2022, doi: <a href="https://doi.org/10.37626/GA9783959872089.0">https://doi.org/10.37626/GA9783959872089.0</a>.'
  mla: Werth, Gerda. “Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde
    Vaertings.” <i>Beiträge zum Mathematikunterricht</i>, WTM, 2022, doi:<a href="https://doi.org/10.37626/GA9783959872089.0">https://doi.org/10.37626/GA9783959872089.0</a>.
  short: 'G. Werth, in: Beiträge zum Mathematikunterricht, WTM, Münster, 2022.'
conference:
  end_date: 2022-09-02
  location: Frankfurt am. Main
  name: 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik
  start_date: 2022-08-29
date_created: 2024-03-14T11:17:56Z
date_updated: 2024-04-09T10:56:58Z
department:
- _id: '10'
- _id: '98'
- _id: '360'
doi: https://doi.org/10.37626/GA9783959872089.0
language:
- iso: ger
place: Münster
publication: Beiträge zum Mathematikunterricht
publication_status: published
publisher: WTM
status: public
title: Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde Vaertings
type: conference
user_id: '578'
year: '2022'
...