---
_id: '63435'
author:
- first_name: Leander
  full_name: Claes, Leander
  id: '11829'
  last_name: Claes
  orcid: 0000-0002-4393-268X
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: 'Claes L, Winkler M. Describing smooth small-data solutions to a quasilinear
    hyperbolic-parabolic system by W 1,P energy analysis. <i>Nonlinear Analysis: Real
    World Applications</i>. 2026;91:104580. doi:<a href="https://doi.org/10.1016/j.nonrwa.2025.104580">10.1016/j.nonrwa.2025.104580</a>'
  apa: 'Claes, L., &#38; Winkler, M. (2026). Describing smooth small-data solutions
    to a quasilinear hyperbolic-parabolic system by W 1,P energy analysis. <i>Nonlinear
    Analysis: Real World Applications</i>, <i>91</i>, 104580. <a href="https://doi.org/10.1016/j.nonrwa.2025.104580">https://doi.org/10.1016/j.nonrwa.2025.104580</a>'
  bibtex: '@article{Claes_Winkler_2026, title={Describing smooth small-data solutions
    to a quasilinear hyperbolic-parabolic system by W 1,P energy analysis}, volume={91},
    DOI={<a href="https://doi.org/10.1016/j.nonrwa.2025.104580">10.1016/j.nonrwa.2025.104580</a>},
    journal={Nonlinear Analysis: Real World Applications}, publisher={Elsevier BV},
    author={Claes, Leander and Winkler, Michael}, year={2026}, pages={104580} }'
  chicago: 'Claes, Leander, and Michael Winkler. “Describing Smooth Small-Data Solutions
    to a Quasilinear Hyperbolic-Parabolic System by W 1,P Energy Analysis.” <i>Nonlinear
    Analysis: Real World Applications</i> 91 (2026): 104580. <a href="https://doi.org/10.1016/j.nonrwa.2025.104580">https://doi.org/10.1016/j.nonrwa.2025.104580</a>.'
  ieee: 'L. Claes and M. Winkler, “Describing smooth small-data solutions to a quasilinear
    hyperbolic-parabolic system by W 1,P energy analysis,” <i>Nonlinear Analysis:
    Real World Applications</i>, vol. 91, p. 104580, 2026, doi: <a href="https://doi.org/10.1016/j.nonrwa.2025.104580">10.1016/j.nonrwa.2025.104580</a>.'
  mla: 'Claes, Leander, and Michael Winkler. “Describing Smooth Small-Data Solutions
    to a Quasilinear Hyperbolic-Parabolic System by W 1,P Energy Analysis.” <i>Nonlinear
    Analysis: Real World Applications</i>, vol. 91, Elsevier BV, 2026, p. 104580,
    doi:<a href="https://doi.org/10.1016/j.nonrwa.2025.104580">10.1016/j.nonrwa.2025.104580</a>.'
  short: 'L. Claes, M. Winkler, Nonlinear Analysis: Real World Applications 91 (2026)
    104580.'
date_created: 2026-01-05T07:32:00Z
date_updated: 2026-01-05T07:40:49Z
department:
- _id: '49'
- _id: '90'
doi: 10.1016/j.nonrwa.2025.104580
intvolume: '        91'
language:
- iso: eng
page: '104580'
project:
- _id: '245'
  name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken
    für Leistungsschallanwendungen (NEPTUN)'
publication: 'Nonlinear Analysis: Real World Applications'
publication_identifier:
  issn:
  - 1468-1218
publisher: Elsevier BV
status: public
title: Describing smooth small-data solutions to a quasilinear hyperbolic-parabolic
  system by W 1,P energy analysis
type: journal_article
user_id: '11829'
volume: 91
year: '2026'
...
---
_id: '65625'
author:
- first_name: Olga
  full_name: Friesen, Olga
  id: '44026'
  last_name: Friesen
- first_name: Jonas
  full_name: Hölscher, Jonas
  id: '73952'
  last_name: Hölscher
- first_name: Michael B. K.
  full_name: Siegmund, Michael B. K.
  last_name: Siegmund
- first_name: Leander
  full_name: Claes, Leander
  id: '11829'
  last_name: Claes
  orcid: 0000-0002-4393-268X
- first_name: Bernd
  full_name: Henning, Bernd
  id: '213'
  last_name: Henning
citation:
  ama: 'Friesen O, Hölscher J, Siegmund MBK, Claes L, Henning B. Experimental and
    Numerical Investigation of Jump Phenomena in the Frequency Response of Piezoelectric
    Systems. In: ; 2026.'
  apa: Friesen, O., Hölscher, J., Siegmund, M. B. K., Claes, L., &#38; Henning, B.
    (2026). <i>Experimental and Numerical Investigation of Jump Phenomena in the Frequency
    Response of Piezoelectric Systems</i>.
  bibtex: '@inproceedings{Friesen_Hölscher_Siegmund_Claes_Henning_2026, place={96th
    Annual Meeting of the International Association of Applied Mathematics and Mechanics
    (GAMM)}, title={Experimental and Numerical Investigation of Jump Phenomena in
    the Frequency Response of Piezoelectric Systems}, author={Friesen, Olga and Hölscher,
    Jonas and Siegmund, Michael B. K. and Claes, Leander and Henning, Bernd}, year={2026}
    }'
  chicago: Friesen, Olga, Jonas Hölscher, Michael B. K. Siegmund, Leander Claes, and
    Bernd Henning. “Experimental and Numerical Investigation of Jump Phenomena in
    the Frequency Response of Piezoelectric Systems.” 96th Annual Meeting of the International
    Association of Applied Mathematics and Mechanics (GAMM), 2026.
  ieee: O. Friesen, J. Hölscher, M. B. K. Siegmund, L. Claes, and B. Henning, “Experimental
    and Numerical Investigation of Jump Phenomena in the Frequency Response of Piezoelectric
    Systems,” 2026.
  mla: Friesen, Olga, et al. <i>Experimental and Numerical Investigation of Jump Phenomena
    in the Frequency Response of Piezoelectric Systems</i>. 2026.
  short: 'O. Friesen, J. Hölscher, M.B.K. Siegmund, L. Claes, B. Henning, in: 96th
    Annual Meeting of the International Association of Applied Mathematics and Mechanics
    (GAMM), 2026.'
date_created: 2026-05-13T14:24:34Z
date_updated: 2026-05-13T14:25:54Z
department:
- _id: '49'
language:
- iso: eng
place: 96th Annual Meeting of the International Association of Applied Mathematics
  and Mechanics (GAMM)
project:
- _id: '245'
  name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken
    für Leistungsschallanwendungen (NEPTUN)'
status: public
title: Experimental and Numerical Investigation of Jump Phenomena in the Frequency
  Response of Piezoelectric Systems
type: conference_abstract
user_id: '44026'
year: '2026'
...
---
_id: '65785'
abstract:
- lang: eng
  text: Simulation-based design of high-power ultrasonic systems depends on the accurate
    modelling of the electromechanical behaviour of piezoceramic materials. In practical
    transducer applications, the relevant operating points are influenced by mechanical
    preload and heating, both of which give rise to changes in the elastic, dielectric,
    and piezoelectric material properties. Material parameters identified under idealised,
    unloaded conditions are therefore insufficient to represent piezoceramic material
    behaviour under realistic operating conditions. To overcome this limitation, experimental
    setups are developed that enable the measurement of electrical impedance spectra
    under controlled thermal and mechanical conditions. The acquired impedance data
    are used in an inverse identification procedure, in which the behaviour of a finite
    element forward model is iteratively fitted to the measurements using a block
    coordinate descent optimisation strategy guided by a sensitivity analysis. This
    yields effective linear material parameters as a function of temperature and mechanical
    stress at varying operating points. The identified temperature-dependent parameters,
    for instance, can be employed in a coupled thermo-electromechanical simulation
    framework to predict the temperature-dependent material behaviour during operation.
    The linear identification based on varying operation points provides an initial
    approximation of the nonlinear material response, establishing a basis for the
    development of corresponding nonlinear material models.
author:
- first_name: Olga
  full_name: Friesen, Olga
  id: '44026'
  last_name: Friesen
  orcid: 0009-0007-5598-9484
- first_name: Leander
  full_name: Claes, Leander
  id: '11829'
  last_name: Claes
  orcid: 0000-0002-4393-268X
- first_name: Jonas
  full_name: Hölscher, Jonas
  id: '73952'
  last_name: Hölscher
- first_name: Bernd
  full_name: Henning, Bernd
  id: '213'
  last_name: Henning
- first_name: Claus
  full_name: Scheidemann, Claus
  id: '38259'
  last_name: Scheidemann
- first_name: Tobias
  full_name: Hemsel, Tobias
  id: '210'
  last_name: Hemsel
- first_name: Raphael
  full_name: Kuess, Raphael
  last_name: Kuess
- first_name: Andrea
  full_name: Walther, Andrea
  last_name: Walther
- first_name: Carsten
  full_name: Spieker, Carsten
  id: '67587'
  last_name: Spieker
- first_name: Jens
  full_name: Förstner, Jens
  id: '158'
  last_name: Förstner
  orcid: 0000-0001-7059-9862
citation:
  ama: Friesen O, Claes L, Hölscher J, et al. Measurement of multiphysical material
    parameters of piezoceramic components for high-power ultrasonic applications.
    <i>tm - Technisches Messen</i>. Published online 2026. doi:<a href="https://doi.org/10.1515/teme-2026-0042">10.1515/teme-2026-0042</a>
  apa: Friesen, O., Claes, L., Hölscher, J., Henning, B., Scheidemann, C., Hemsel,
    T., Kuess, R., Walther, A., Spieker, C., &#38; Förstner, J. (2026). Measurement
    of multiphysical material parameters of piezoceramic components for high-power
    ultrasonic applications. <i>Tm - Technisches Messen</i>. <a href="https://doi.org/10.1515/teme-2026-0042">https://doi.org/10.1515/teme-2026-0042</a>
  bibtex: '@article{Friesen_Claes_Hölscher_Henning_Scheidemann_Hemsel_Kuess_Walther_Spieker_Förstner_2026,
    title={Measurement of multiphysical material parameters of piezoceramic components
    for high-power ultrasonic applications}, DOI={<a href="https://doi.org/10.1515/teme-2026-0042">10.1515/teme-2026-0042</a>},
    journal={tm - Technisches Messen}, publisher={Walter de Gruyter GmbH}, author={Friesen,
    Olga and Claes, Leander and Hölscher, Jonas and Henning, Bernd and Scheidemann,
    Claus and Hemsel, Tobias and Kuess, Raphael and Walther, Andrea and Spieker, Carsten
    and Förstner, Jens}, year={2026} }'
  chicago: Friesen, Olga, Leander Claes, Jonas Hölscher, Bernd Henning, Claus Scheidemann,
    Tobias Hemsel, Raphael Kuess, Andrea Walther, Carsten Spieker, and Jens Förstner.
    “Measurement of Multiphysical Material Parameters of Piezoceramic Components for High-Power
    Ultrasonic Applications.” <i>Tm - Technisches Messen</i>, 2026. <a href="https://doi.org/10.1515/teme-2026-0042">https://doi.org/10.1515/teme-2026-0042</a>.
  ieee: 'O. Friesen <i>et al.</i>, “Measurement of multiphysical material parameters
    of piezoceramic components for high-power ultrasonic applications,” <i>tm - Technisches
    Messen</i>, 2026, doi: <a href="https://doi.org/10.1515/teme-2026-0042">10.1515/teme-2026-0042</a>.'
  mla: Friesen, Olga, et al. “Measurement of Multiphysical Material Parameters of Piezoceramic
    Components for High-Power Ultrasonic Applications.” <i>Tm - Technisches Messen</i>,
    Walter de Gruyter GmbH, 2026, doi:<a href="https://doi.org/10.1515/teme-2026-0042">10.1515/teme-2026-0042</a>.
  short: O. Friesen, L. Claes, J. Hölscher, B. Henning, C. Scheidemann, T. Hemsel,
    R. Kuess, A. Walther, C. Spieker, J. Förstner, Tm - Technisches Messen (2026).
date_created: 2026-06-08T05:44:09Z
date_updated: 2026-06-08T17:54:45Z
department:
- _id: '49'
doi: 10.1515/teme-2026-0042
keyword:
- tet_topic_piezo
language:
- iso: eng
main_file_link:
- open_access: '1'
oa: '1'
project:
- _id: '245'
  name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken
    für Leistungsschallanwendungen (NEPTUN)'
publication: tm - Technisches Messen
publication_identifier:
  issn:
  - 0171-8096
  - 2196-7113
publication_status: published
publisher: Walter de Gruyter GmbH
status: public
title: Measurement of multiphysical material parameters of piezoceramic components
  for high-power ultrasonic applications
type: journal_article
user_id: '158'
year: '2026'
...
---
_id: '65588'
author:
- first_name: Carsten
  full_name: Spieker, Carsten
  id: '67587'
  last_name: Spieker
- first_name: Raphael
  full_name: Kuess, Raphael
  last_name: Kuess
- first_name: Andrea
  full_name: Walther, Andrea
  last_name: Walther
- first_name: Jens
  full_name: Förstner, Jens
  id: '158'
  last_name: Förstner
  orcid: 0000-0001-7059-9862
citation:
  ama: 'Spieker C, Kuess R, Walther A, Förstner J. Modellierung und Simulation des
    temperaturabhängigen Materialverhaltens von Piezokeramiken mit FEniCS. In: Deutsche
    Gesellschaft für Akustik e.V., ed. <i>Fortschritte Der Akustik - DAGA 2026</i>.
    ; 2026:1066–1069. doi:<a href="https://doi.org/10.71568/DAGA2026.549">10.71568/DAGA2026.549</a>'
  apa: Spieker, C., Kuess, R., Walther, A., &#38; Förstner, J. (2026). Modellierung
    und Simulation des temperaturabhängigen Materialverhaltens von Piezokeramiken
    mit FEniCS. In Deutsche Gesellschaft für Akustik e.V. (Ed.), <i>Fortschritte der
    Akustik - DAGA 2026</i> (pp. 1066–1069). <a href="https://doi.org/10.71568/DAGA2026.549">https://doi.org/10.71568/DAGA2026.549</a>
  bibtex: '@inproceedings{Spieker_Kuess_Walther_Förstner_2026, title={Modellierung
    und Simulation des temperaturabhängigen Materialverhaltens von Piezokeramiken
    mit FEniCS}, DOI={<a href="https://doi.org/10.71568/DAGA2026.549">10.71568/DAGA2026.549</a>},
    booktitle={Fortschritte der Akustik - DAGA 2026}, author={Spieker, Carsten and
    Kuess, Raphael and Walther, Andrea and Förstner, Jens}, editor={Deutsche Gesellschaft
    für Akustik e.V.}, year={2026}, pages={1066–1069} }'
  chicago: Spieker, Carsten, Raphael Kuess, Andrea Walther, and Jens Förstner. “Modellierung
    Und Simulation Des Temperaturabhängigen Materialverhaltens von Piezokeramiken
    Mit FEniCS.” In <i>Fortschritte Der Akustik - DAGA 2026</i>, edited by Deutsche
    Gesellschaft für Akustik e.V., 1066–1069, 2026. <a href="https://doi.org/10.71568/DAGA2026.549">https://doi.org/10.71568/DAGA2026.549</a>.
  ieee: 'C. Spieker, R. Kuess, A. Walther, and J. Förstner, “Modellierung und Simulation
    des temperaturabhängigen Materialverhaltens von Piezokeramiken mit FEniCS,” in
    <i>Fortschritte der Akustik - DAGA 2026</i>, 2026, pp. 1066–1069, doi: <a href="https://doi.org/10.71568/DAGA2026.549">10.71568/DAGA2026.549</a>.'
  mla: Spieker, Carsten, et al. “Modellierung Und Simulation Des Temperaturabhängigen
    Materialverhaltens von Piezokeramiken Mit FEniCS.” <i>Fortschritte Der Akustik
    - DAGA 2026</i>, edited by Deutsche Gesellschaft für Akustik e.V., 2026, pp. 1066–1069,
    doi:<a href="https://doi.org/10.71568/DAGA2026.549">10.71568/DAGA2026.549</a>.
  short: 'C. Spieker, R. Kuess, A. Walther, J. Förstner, in: Deutsche Gesellschaft
    für Akustik e.V. (Ed.), Fortschritte Der Akustik - DAGA 2026, 2026, pp. 1066–1069.'
corporate_editor:
- Deutsche Gesellschaft für Akustik e.V.
date_created: 2026-05-08T12:37:35Z
date_updated: 2026-06-08T17:55:18Z
department:
- _id: '61'
doi: 10.71568/DAGA2026.549
keyword:
- tet_topic_piezo
language:
- iso: eng
page: 1066–1069
project:
- _id: '245'
  name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken
    für Leistungsschallanwendungen (NEPTUN)'
publication: Fortschritte der Akustik - DAGA 2026
status: public
title: Modellierung und Simulation des temperaturabhängigen Materialverhaltens von
  Piezokeramiken mit FEniCS
type: conference
user_id: '158'
year: '2026'
...
---
_id: '66060'
author:
- first_name: Leander
  full_name: Claes, Leander
  id: '11829'
  last_name: Claes
  orcid: 0000-0002-4393-268X
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Claes L, Winkler M. Local strong solutions in a quasilinear Moore-Gibson-Thompson
    type model for thermoviscoelastic evolution in a standard linear solid. <i>Nonlinear
    Differential Equations and Applications NoDEA</i>. 2026;33(4). doi:<a href="https://doi.org/10.1007/s00030-026-01239-7">10.1007/s00030-026-01239-7</a>
  apa: Claes, L., &#38; Winkler, M. (2026). Local strong solutions in a quasilinear
    Moore-Gibson-Thompson type model for thermoviscoelastic evolution in a standard
    linear solid. <i>Nonlinear Differential Equations and Applications NoDEA</i>,
    <i>33</i>(4). <a href="https://doi.org/10.1007/s00030-026-01239-7">https://doi.org/10.1007/s00030-026-01239-7</a>
  bibtex: '@article{Claes_Winkler_2026, title={Local strong solutions in a quasilinear
    Moore-Gibson-Thompson type model for thermoviscoelastic evolution in a standard
    linear solid}, volume={33}, DOI={<a href="https://doi.org/10.1007/s00030-026-01239-7">10.1007/s00030-026-01239-7</a>},
    number={4}, journal={Nonlinear Differential Equations and Applications NoDEA},
    publisher={Springer Science and Business Media LLC}, author={Claes, Leander and
    Winkler, Michael}, year={2026} }'
  chicago: Claes, Leander, and Michael Winkler. “Local Strong Solutions in a Quasilinear
    Moore-Gibson-Thompson Type Model for Thermoviscoelastic Evolution in a Standard
    Linear Solid.” <i>Nonlinear Differential Equations and Applications NoDEA</i>
    33, no. 4 (2026). <a href="https://doi.org/10.1007/s00030-026-01239-7">https://doi.org/10.1007/s00030-026-01239-7</a>.
  ieee: 'L. Claes and M. Winkler, “Local strong solutions in a quasilinear Moore-Gibson-Thompson
    type model for thermoviscoelastic evolution in a standard linear solid,” <i>Nonlinear
    Differential Equations and Applications NoDEA</i>, vol. 33, no. 4, 2026, doi:
    <a href="https://doi.org/10.1007/s00030-026-01239-7">10.1007/s00030-026-01239-7</a>.'
  mla: Claes, Leander, and Michael Winkler. “Local Strong Solutions in a Quasilinear
    Moore-Gibson-Thompson Type Model for Thermoviscoelastic Evolution in a Standard
    Linear Solid.” <i>Nonlinear Differential Equations and Applications NoDEA</i>,
    vol. 33, no. 4, Springer Science and Business Media LLC, 2026, doi:<a href="https://doi.org/10.1007/s00030-026-01239-7">10.1007/s00030-026-01239-7</a>.
  short: L. Claes, M. Winkler, Nonlinear Differential Equations and Applications NoDEA
    33 (2026).
date_created: 2026-06-26T09:21:21Z
date_updated: 2026-06-26T09:23:14Z
department:
- _id: '49'
- _id: '90'
doi: 10.1007/s00030-026-01239-7
intvolume: '        33'
issue: '4'
language:
- iso: eng
project:
- _id: '245'
  name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken
    für Leistungsschallanwendungen (NEPTUN)'
publication: Nonlinear Differential Equations and Applications NoDEA
publication_identifier:
  issn:
  - 1420-9004
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Local strong solutions in a quasilinear Moore-Gibson-Thompson type model for
  thermoviscoelastic evolution in a standard linear solid
type: journal_article
user_id: '11829'
volume: 33
year: '2026'
...
---
_id: '66604'
author:
- first_name: Olga
  full_name: Friesen, Olga
  id: '44026'
  last_name: Friesen
  orcid: 0009-0007-5598-9484
- first_name: Jonas
  full_name: Hölscher, Jonas
  id: '73952'
  last_name: Hölscher
- first_name: Carsten
  full_name: Spieker, Carsten
  id: '67587'
  last_name: Spieker
- first_name: Jens
  full_name: Förstner, Jens
  id: '158'
  last_name: Förstner
  orcid: 0000-0001-7059-9862
- first_name: Leander
  full_name: Claes, Leander
  id: '11829'
  last_name: Claes
  orcid: 0000-0002-4393-268X
citation:
  ama: 'Friesen O, Hölscher J, Spieker C, Förstner J, Claes L. Quantitative Modelling
    of Dynamic Nonlinearity in Piezoelectric Components. In: ; 2026.'
  apa: Friesen, O., Hölscher, J., Spieker, C., Förstner, J., &#38; Claes, L. (2026).
    <i>Quantitative Modelling of Dynamic Nonlinearity in Piezoelectric Components</i>.
    WCCM-ECCOMAS 2026, München.
  bibtex: '@inproceedings{Friesen_Hölscher_Spieker_Förstner_Claes_2026, title={Quantitative
    Modelling of Dynamic Nonlinearity in Piezoelectric Components}, author={Friesen,
    Olga and Hölscher, Jonas and Spieker, Carsten and Förstner, Jens and Claes, Leander},
    year={2026} }'
  chicago: Friesen, Olga, Jonas Hölscher, Carsten Spieker, Jens Förstner, and Leander
    Claes. “Quantitative Modelling of Dynamic Nonlinearity in Piezoelectric Components,”
    2026.
  ieee: O. Friesen, J. Hölscher, C. Spieker, J. Förstner, and L. Claes, “Quantitative
    Modelling of Dynamic Nonlinearity in Piezoelectric Components,” presented at the
    WCCM-ECCOMAS 2026, München, 2026.
  mla: Friesen, Olga, et al. <i>Quantitative Modelling of Dynamic Nonlinearity in
    Piezoelectric Components</i>. 2026.
  short: 'O. Friesen, J. Hölscher, C. Spieker, J. Förstner, L. Claes, in: 2026.'
conference:
  end_date: 2026-07-24
  location: München
  name: WCCM-ECCOMAS 2026
  start_date: 2026-07-19
date_created: 2026-07-27T15:07:31Z
date_updated: 2026-07-27T15:08:16Z
department:
- _id: '49'
language:
- iso: eng
project:
- _id: '245'
  name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken
    für Leistungsschallanwendungen (NEPTUN)'
status: public
title: Quantitative Modelling of Dynamic Nonlinearity in Piezoelectric Components
type: conference_abstract
user_id: '44026'
year: '2026'
...
---
_id: '62300'
author:
- first_name: Leander
  full_name: Claes, Leander
  id: '11829'
  last_name: Claes
  orcid: 0000-0002-4393-268X
- first_name: Jonas
  full_name: Hölscher, Jonas
  id: '73952'
  last_name: Hölscher
- first_name: Olga
  full_name: Friesen, Olga
  id: '44026'
  last_name: Friesen
- first_name: Claus
  full_name: Scheidemann, Claus
  id: '38259'
  last_name: Scheidemann
- first_name: Tobias
  full_name: Hemsel, Tobias
  id: '210'
  last_name: Hemsel
- first_name: Bernd
  full_name: Henning, Bernd
  id: '213'
  last_name: Henning
citation:
  ama: 'Claes L, Hölscher J, Friesen O, Scheidemann C, Hemsel T, Henning B. Estimation
    of third order elastic constants of piezoceramics using DC biased impedance measurements.
    In: <i>2025 International Congress on Ultrasonics</i>. AMA Service GmbH; 2025:142–145.
    doi:<a href="https://doi.org/10.5162/ultrasonic2025/a18-a6">10.5162/ultrasonic2025/a18-a6</a>'
  apa: Claes, L., Hölscher, J., Friesen, O., Scheidemann, C., Hemsel, T., &#38; Henning,
    B. (2025). Estimation of third order elastic constants of piezoceramics using
    DC biased impedance measurements. <i>2025 International Congress on Ultrasonics</i>,
    142–145. <a href="https://doi.org/10.5162/ultrasonic2025/a18-a6">https://doi.org/10.5162/ultrasonic2025/a18-a6</a>
  bibtex: '@inproceedings{Claes_Hölscher_Friesen_Scheidemann_Hemsel_Henning_2025,
    place={Paderborn}, title={Estimation of third order elastic constants of piezoceramics
    using DC biased impedance measurements}, DOI={<a href="https://doi.org/10.5162/ultrasonic2025/a18-a6">10.5162/ultrasonic2025/a18-a6</a>},
    booktitle={2025 International Congress on Ultrasonics}, publisher={AMA Service
    GmbH}, author={Claes, Leander and Hölscher, Jonas and Friesen, Olga and Scheidemann,
    Claus and Hemsel, Tobias and Henning, Bernd}, year={2025}, pages={142–145} }'
  chicago: 'Claes, Leander, Jonas Hölscher, Olga Friesen, Claus Scheidemann, Tobias
    Hemsel, and Bernd Henning. “Estimation of Third Order Elastic Constants of Piezoceramics
    Using DC Biased Impedance Measurements.” In <i>2025 International Congress on
    Ultrasonics</i>, 142–145. Paderborn: AMA Service GmbH, 2025. <a href="https://doi.org/10.5162/ultrasonic2025/a18-a6">https://doi.org/10.5162/ultrasonic2025/a18-a6</a>.'
  ieee: 'L. Claes, J. Hölscher, O. Friesen, C. Scheidemann, T. Hemsel, and B. Henning,
    “Estimation of third order elastic constants of piezoceramics using DC biased
    impedance measurements,” in <i>2025 International Congress on Ultrasonics</i>,
    2025, pp. 142–145, doi: <a href="https://doi.org/10.5162/ultrasonic2025/a18-a6">10.5162/ultrasonic2025/a18-a6</a>.'
  mla: Claes, Leander, et al. “Estimation of Third Order Elastic Constants of Piezoceramics
    Using DC Biased Impedance Measurements.” <i>2025 International Congress on Ultrasonics</i>,
    AMA Service GmbH, 2025, pp. 142–145, doi:<a href="https://doi.org/10.5162/ultrasonic2025/a18-a6">10.5162/ultrasonic2025/a18-a6</a>.
  short: 'L. Claes, J. Hölscher, O. Friesen, C. Scheidemann, T. Hemsel, B. Henning,
    in: 2025 International Congress on Ultrasonics, AMA Service GmbH, Paderborn, 2025,
    pp. 142–145.'
date_created: 2025-11-25T12:23:06Z
date_updated: 2026-01-13T13:00:31Z
department:
- _id: '49'
doi: 10.5162/ultrasonic2025/a18-a6
language:
- iso: eng
page: 142–145
place: Paderborn
project:
- _id: '245'
  name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken
    für Leistungsschallanwendungen (NEPTUN)'
publication: 2025 International Congress on Ultrasonics
publisher: AMA Service GmbH
status: public
title: Estimation of third order elastic constants of piezoceramics using DC biased
  impedance measurements
type: conference
user_id: '11829'
year: '2025'
...
---
_id: '59258'
article_number: '44'
author:
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Winkler M. Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity
    with Temperature-Dependent Parameters. <i>Applied Mathematics &#38; Optimization</i>.
    2025;91(2). doi:<a href="https://doi.org/10.1007/s00245-025-10243-9">10.1007/s00245-025-10243-9</a>
  apa: Winkler, M. (2025). Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity
    with Temperature-Dependent Parameters. <i>Applied Mathematics &#38; Optimization</i>,
    <i>91</i>(2), Article 44. <a href="https://doi.org/10.1007/s00245-025-10243-9">https://doi.org/10.1007/s00245-025-10243-9</a>
  bibtex: '@article{Winkler_2025, title={Rough Data in an Evolution System Generalizing
    1D Thermoviscoelasticity with Temperature-Dependent Parameters}, volume={91},
    DOI={<a href="https://doi.org/10.1007/s00245-025-10243-9">10.1007/s00245-025-10243-9</a>},
    number={244}, journal={Applied Mathematics &#38; Optimization}, publisher={Springer
    Science and Business Media LLC}, author={Winkler, Michael}, year={2025} }'
  chicago: Winkler, Michael. “Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity
    with Temperature-Dependent Parameters.” <i>Applied Mathematics &#38; Optimization</i>
    91, no. 2 (2025). <a href="https://doi.org/10.1007/s00245-025-10243-9">https://doi.org/10.1007/s00245-025-10243-9</a>.
  ieee: 'M. Winkler, “Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity
    with Temperature-Dependent Parameters,” <i>Applied Mathematics &#38; Optimization</i>,
    vol. 91, no. 2, Art. no. 44, 2025, doi: <a href="https://doi.org/10.1007/s00245-025-10243-9">10.1007/s00245-025-10243-9</a>.'
  mla: Winkler, Michael. “Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity
    with Temperature-Dependent Parameters.” <i>Applied Mathematics &#38; Optimization</i>,
    vol. 91, no. 2, 44, Springer Science and Business Media LLC, 2025, doi:<a href="https://doi.org/10.1007/s00245-025-10243-9">10.1007/s00245-025-10243-9</a>.
  short: M. Winkler, Applied Mathematics &#38; Optimization 91 (2025).
date_created: 2025-04-02T11:23:25Z
date_updated: 2026-02-26T15:59:30Z
department:
- _id: '90'
doi: 10.1007/s00245-025-10243-9
intvolume: '        91'
issue: '2'
language:
- iso: eng
project:
- _id: '245'
  name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken
    für Leistungsschallanwendungen (NEPTUN)'
publication: Applied Mathematics & Optimization
publication_identifier:
  issn:
  - 0095-4616
  - 1432-0606
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with
  Temperature-Dependent Parameters
type: journal_article
user_id: '11829'
volume: 91
year: '2025'
...
---
_id: '61755'
author:
- first_name: Claus
  full_name: Scheidemann, Claus
  id: '38259'
  last_name: Scheidemann
- first_name: Tobias
  full_name: Hemsel, Tobias
  id: '210'
  last_name: Hemsel
- first_name: Walter
  full_name: Sextro, Walter
  id: '21220'
  last_name: Sextro
citation:
  ama: 'Scheidemann C, Hemsel T, Sextro W. Time dependent material characteristics
    of prestressed piezoelectric ceramics in langevin transducers. In: ; 2025.'
  apa: Scheidemann, C., Hemsel, T., &#38; Sextro, W. (2025). <i>Time dependent material
    characteristics of prestressed piezoelectric ceramics in langevin transducers</i>.
    22nd International Workshop on Piezoelectric Materials and Applications in Actuators
    (IWPMA), Vilnius, Lithuania.
  bibtex: '@inproceedings{Scheidemann_Hemsel_Sextro_2025, title={Time dependent material
    characteristics of prestressed piezoelectric ceramics in langevin transducers},
    author={Scheidemann, Claus and Hemsel, Tobias and Sextro, Walter}, year={2025}
    }'
  chicago: Scheidemann, Claus, Tobias Hemsel, and Walter Sextro. “Time Dependent Material
    Characteristics of Prestressed Piezoelectric Ceramics in Langevin Transducers,”
    2025.
  ieee: C. Scheidemann, T. Hemsel, and W. Sextro, “Time dependent material characteristics
    of prestressed piezoelectric ceramics in langevin transducers,” presented at the
    22nd International Workshop on Piezoelectric Materials and Applications in Actuators
    (IWPMA), Vilnius, Lithuania, 2025.
  mla: Scheidemann, Claus, et al. <i>Time Dependent Material Characteristics of Prestressed
    Piezoelectric Ceramics in Langevin Transducers</i>. 2025.
  short: 'C. Scheidemann, T. Hemsel, W. Sextro, in: 2025.'
conference:
  end_date: 2025-07-3
  location: Vilnius, Lithuania
  name: 22nd International Workshop on Piezoelectric Materials and Applications in
    Actuators (IWPMA)
  start_date: 2025-07-1
date_created: 2025-10-08T14:22:32Z
date_updated: 2026-03-02T10:59:53Z
ddc:
- '620'
department:
- _id: '151'
file:
- access_level: open_access
  content_type: application/pdf
  creator: hemsel
  date_created: 2026-01-30T11:07:48Z
  date_updated: 2026-03-02T10:59:53Z
  file_id: '63817'
  file_name: SHS25_IWPMA_2025.pdf
  file_size: 644147
  relation: main_file
file_date_updated: 2026-03-02T10:59:53Z
has_accepted_license: '1'
language:
- iso: eng
oa: '1'
project:
- _id: '245'
  name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken
    für Leistungsschallanwendungen (NEPTUN)'
status: public
title: Time dependent material characteristics of prestressed piezoelectric ceramics
  in langevin transducers
type: conference
user_id: '210'
year: '2025'
...
---
_id: '61757'
author:
- first_name: Claus
  full_name: Scheidemann, Claus
  id: '38259'
  last_name: Scheidemann
- first_name: Julius
  full_name: Porzenheim, Julius
  last_name: Porzenheim
- first_name: Tobias
  full_name: Hemsel, Tobias
  id: '210'
  last_name: Hemsel
- first_name: Walter
  full_name: Sextro, Walter
  id: '21220'
  last_name: Sextro
citation:
  ama: 'Scheidemann C, Porzenheim J, Hemsel T, Sextro W. Investigation of the Setting
    Behaviour of Mechanically Biased Piezoelectric Ultrasonic Transducers. In: ; 2025.'
  apa: Scheidemann, C., Porzenheim, J., Hemsel, T., &#38; Sextro, W. (2025). <i>Investigation
    of the Setting Behaviour of Mechanically Biased Piezoelectric Ultrasonic Transducers</i>.
    2025 International Congress on Ultrasonics (ICU), Paderborn, Germany.
  bibtex: '@inproceedings{Scheidemann_Porzenheim_Hemsel_Sextro_2025, title={Investigation
    of the Setting Behaviour of Mechanically Biased Piezoelectric Ultrasonic Transducers},
    author={Scheidemann, Claus and Porzenheim, Julius and Hemsel, Tobias and Sextro,
    Walter}, year={2025} }'
  chicago: Scheidemann, Claus, Julius Porzenheim, Tobias Hemsel, and Walter Sextro.
    “Investigation of the Setting Behaviour of Mechanically Biased Piezoelectric Ultrasonic
    Transducers,” 2025.
  ieee: C. Scheidemann, J. Porzenheim, T. Hemsel, and W. Sextro, “Investigation of
    the Setting Behaviour of Mechanically Biased Piezoelectric Ultrasonic Transducers,”
    presented at the 2025 International Congress on Ultrasonics (ICU), Paderborn,
    Germany, 2025.
  mla: Scheidemann, Claus, et al. <i>Investigation of the Setting Behaviour of Mechanically
    Biased Piezoelectric Ultrasonic Transducers</i>. 2025.
  short: 'C. Scheidemann, J. Porzenheim, T. Hemsel, W. Sextro, in: 2025.'
conference:
  end_date: 2025-09-25
  location: Paderborn, Germany
  name: 2025 International Congress on Ultrasonics (ICU)
  start_date: 2025-09-21
date_created: 2025-10-08T14:33:44Z
date_updated: 2026-03-02T10:59:36Z
ddc:
- '620'
department:
- _id: '151'
file:
- access_level: open_access
  content_type: application/pdf
  creator: hemsel
  date_created: 2026-01-30T07:30:44Z
  date_updated: 2026-03-02T10:59:36Z
  file_id: '63816'
  file_name: Sch25_ICU_2025.pdf
  file_size: 783790
  relation: main_file
file_date_updated: 2026-03-02T10:59:36Z
has_accepted_license: '1'
language:
- iso: eng
oa: '1'
project:
- _id: '245'
  name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken
    für Leistungsschallanwendungen (NEPTUN)'
status: public
title: Investigation of the Setting Behaviour of Mechanically Biased Piezoelectric
  Ultrasonic Transducers
type: conference
user_id: '210'
year: '2025'
...
---
_id: '62000'
article_type: original
author:
- first_name: Leander
  full_name: Claes, Leander
  id: '11829'
  last_name: Claes
  orcid: 0000-0002-4393-268X
- first_name: Kevin
  full_name: Koch, Kevin
  last_name: Koch
- first_name: Olga
  full_name: Friesen, Olga
  id: '44026'
  last_name: Friesen
- first_name: Lars
  full_name: Meihost, Lars
  id: '24769'
  last_name: Meihost
citation:
  ama: Claes L, Koch K, Friesen O, Meihost L. Machine Learning-Supported Inverse Measurement
    Procedure for Broadband, Temperature Dependent Piezoelectric Material Parameters.
    <i>Acta Acustica</i>. 2025;9(65). doi:<a href="https://doi.org/10.1051/aacus/2025044">10.1051/aacus/2025044</a>
  apa: Claes, L., Koch, K., Friesen, O., &#38; Meihost, L. (2025). Machine Learning-Supported
    Inverse Measurement Procedure for Broadband, Temperature Dependent Piezoelectric
    Material Parameters. <i>Acta Acustica</i>, <i>9</i>(65). <a href="https://doi.org/10.1051/aacus/2025044">https://doi.org/10.1051/aacus/2025044</a>
  bibtex: '@article{Claes_Koch_Friesen_Meihost_2025, title={Machine Learning-Supported
    Inverse Measurement Procedure for Broadband, Temperature Dependent Piezoelectric
    Material Parameters}, volume={9}, DOI={<a href="https://doi.org/10.1051/aacus/2025044">10.1051/aacus/2025044</a>},
    number={65}, journal={Acta Acustica}, publisher={EDP Sciences}, author={Claes,
    Leander and Koch, Kevin and Friesen, Olga and Meihost, Lars}, year={2025} }'
  chicago: Claes, Leander, Kevin Koch, Olga Friesen, and Lars Meihost. “Machine Learning-Supported
    Inverse Measurement Procedure for Broadband, Temperature Dependent Piezoelectric
    Material Parameters.” <i>Acta Acustica</i> 9, no. 65 (2025). <a href="https://doi.org/10.1051/aacus/2025044">https://doi.org/10.1051/aacus/2025044</a>.
  ieee: 'L. Claes, K. Koch, O. Friesen, and L. Meihost, “Machine Learning-Supported
    Inverse Measurement Procedure for Broadband, Temperature Dependent Piezoelectric
    Material Parameters,” <i>Acta Acustica</i>, vol. 9, no. 65, 2025, doi: <a href="https://doi.org/10.1051/aacus/2025044">10.1051/aacus/2025044</a>.'
  mla: Claes, Leander, et al. “Machine Learning-Supported Inverse Measurement Procedure
    for Broadband, Temperature Dependent Piezoelectric Material Parameters.” <i>Acta
    Acustica</i>, vol. 9, no. 65, EDP Sciences, 2025, doi:<a href="https://doi.org/10.1051/aacus/2025044">10.1051/aacus/2025044</a>.
  short: L. Claes, K. Koch, O. Friesen, L. Meihost, Acta Acustica 9 (2025).
date_created: 2025-10-27T08:20:53Z
date_updated: 2026-01-05T08:00:05Z
department:
- _id: '49'
doi: 10.1051/aacus/2025044
intvolume: '         9'
issue: '65'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://acta-acustica.edpsciences.org/articles/aacus/abs/2025/01/aacus250049/aacus250049.html
oa: '1'
project:
- _id: '52'
  name: Computing Resources Provided by the Paderborn Center for Parallel Computing
- _id: '245'
  name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken
    für Leistungsschallanwendungen (NEPTUN)'
publication: Acta Acustica
publication_identifier:
  issn:
  - 2681-4617
publication_status: published
publisher: EDP Sciences
status: public
title: Machine Learning-Supported Inverse Measurement Procedure for Broadband, Temperature
  Dependent Piezoelectric Material Parameters
type: journal_article
user_id: '11829'
volume: 9
year: '2025'
...
---
_id: '54837'
author:
- first_name: Leander
  full_name: Claes, Leander
  id: '11829'
  last_name: Claes
  orcid: 0000-0002-4393-268X
- first_name: Johannes
  full_name: Lankeit, Johannes
  last_name: Lankeit
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: 'Claes L, Lankeit J, Winkler M. A model for heat generation by acoustic waves
    in piezoelectric materials: Global large-data solutions. <i>Mathematical Models
    and Methods in Applied Sciences</i>. 2025;35(11):2465-2512. doi:<a href="https://doi.org/10.1142/s0218202525500447">10.1142/s0218202525500447</a>'
  apa: 'Claes, L., Lankeit, J., &#38; Winkler, M. (2025). A model for heat generation
    by acoustic waves in piezoelectric materials: Global large-data solutions. <i>Mathematical
    Models and Methods in Applied Sciences</i>, <i>35</i>(11), 2465–2512. <a href="https://doi.org/10.1142/s0218202525500447">https://doi.org/10.1142/s0218202525500447</a>'
  bibtex: '@article{Claes_Lankeit_Winkler_2025, title={A model for heat generation
    by acoustic waves in piezoelectric materials: Global large-data solutions}, volume={35},
    DOI={<a href="https://doi.org/10.1142/s0218202525500447">10.1142/s0218202525500447</a>},
    number={11}, journal={Mathematical Models and Methods in Applied Sciences}, publisher={World
    Scientific Pub Co Pte Ltd}, author={Claes, Leander and Lankeit, Johannes and Winkler,
    Michael}, year={2025}, pages={2465–2512} }'
  chicago: 'Claes, Leander, Johannes Lankeit, and Michael Winkler. “A Model for Heat
    Generation by Acoustic Waves in Piezoelectric Materials: Global Large-Data Solutions.”
    <i>Mathematical Models and Methods in Applied Sciences</i> 35, no. 11 (2025):
    2465–2512. <a href="https://doi.org/10.1142/s0218202525500447">https://doi.org/10.1142/s0218202525500447</a>.'
  ieee: 'L. Claes, J. Lankeit, and M. Winkler, “A model for heat generation by acoustic
    waves in piezoelectric materials: Global large-data solutions,” <i>Mathematical
    Models and Methods in Applied Sciences</i>, vol. 35, no. 11, pp. 2465–2512, 2025,
    doi: <a href="https://doi.org/10.1142/s0218202525500447">10.1142/s0218202525500447</a>.'
  mla: 'Claes, Leander, et al. “A Model for Heat Generation by Acoustic Waves in Piezoelectric
    Materials: Global Large-Data Solutions.” <i>Mathematical Models and Methods in
    Applied Sciences</i>, vol. 35, no. 11, World Scientific Pub Co Pte Ltd, 2025,
    pp. 2465–512, doi:<a href="https://doi.org/10.1142/s0218202525500447">10.1142/s0218202525500447</a>.'
  short: L. Claes, J. Lankeit, M. Winkler, Mathematical Models and Methods in Applied
    Sciences 35 (2025) 2465–2512.
date_created: 2024-06-20T13:43:42Z
date_updated: 2026-01-05T07:59:41Z
department:
- _id: '90'
- _id: '49'
doi: 10.1142/s0218202525500447
external_id:
  arxiv:
  - '2411.14900'
intvolume: '        35'
issue: '11'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/pdf/2411.14900
oa: '1'
page: 2465-2512
project:
- _id: '245'
  name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken
    für Leistungsschallanwendungen (NEPTUN)'
publication: Mathematical Models and Methods in Applied Sciences
publication_identifier:
  issn:
  - 1793-6314
publisher: World Scientific Pub Co Pte Ltd
status: public
title: 'A model for heat generation by acoustic waves in piezoelectric materials:
  Global large-data solutions'
type: journal_article
user_id: '11829'
volume: 35
year: '2025'
...
---
_id: '62299'
author:
- first_name: Olga
  full_name: Friesen, Olga
  id: '44026'
  last_name: Friesen
- first_name: Claus
  full_name: Scheidemann, Claus
  id: '38259'
  last_name: Scheidemann
- first_name: Leander
  full_name: Claes, Leander
  id: '11829'
  last_name: Claes
  orcid: 0000-0002-4393-268X
- first_name: Tobias
  full_name: Hemsel, Tobias
  id: '210'
  last_name: Hemsel
- first_name: Bernd
  full_name: Henning, Bernd
  id: '213'
  last_name: Henning
citation:
  ama: 'Friesen O, Scheidemann C, Claes L, Hemsel T, Henning B. Sensitivity Analysis
    and Material Parameter Estimation of a Pre-Stressed Langevin Transducer. In: <i>2025
    International Congress on Ultrasonics</i>. AMA Service GmbH; 2025:138–141. doi:<a
    href="https://doi.org/10.5162/ultrasonic2025/a18-a4">10.5162/ultrasonic2025/a18-a4</a>'
  apa: Friesen, O., Scheidemann, C., Claes, L., Hemsel, T., &#38; Henning, B. (2025).
    Sensitivity Analysis and Material Parameter Estimation of a Pre-Stressed Langevin
    Transducer. <i>2025 International Congress on Ultrasonics</i>, 138–141. <a href="https://doi.org/10.5162/ultrasonic2025/a18-a4">https://doi.org/10.5162/ultrasonic2025/a18-a4</a>
  bibtex: '@inproceedings{Friesen_Scheidemann_Claes_Hemsel_Henning_2025, place={Paderborn},
    title={Sensitivity Analysis and Material Parameter Estimation of a Pre-Stressed
    Langevin Transducer}, DOI={<a href="https://doi.org/10.5162/ultrasonic2025/a18-a4">10.5162/ultrasonic2025/a18-a4</a>},
    booktitle={2025 International Congress on Ultrasonics}, publisher={AMA Service
    GmbH}, author={Friesen, Olga and Scheidemann, Claus and Claes, Leander and Hemsel,
    Tobias and Henning, Bernd}, year={2025}, pages={138–141} }'
  chicago: 'Friesen, Olga, Claus Scheidemann, Leander Claes, Tobias Hemsel, and Bernd
    Henning. “Sensitivity Analysis and Material Parameter Estimation of a Pre-Stressed
    Langevin Transducer.” In <i>2025 International Congress on Ultrasonics</i>, 138–141.
    Paderborn: AMA Service GmbH, 2025. <a href="https://doi.org/10.5162/ultrasonic2025/a18-a4">https://doi.org/10.5162/ultrasonic2025/a18-a4</a>.'
  ieee: 'O. Friesen, C. Scheidemann, L. Claes, T. Hemsel, and B. Henning, “Sensitivity
    Analysis and Material Parameter Estimation of a Pre-Stressed Langevin Transducer,”
    in <i>2025 International Congress on Ultrasonics</i>, 2025, pp. 138–141, doi:
    <a href="https://doi.org/10.5162/ultrasonic2025/a18-a4">10.5162/ultrasonic2025/a18-a4</a>.'
  mla: Friesen, Olga, et al. “Sensitivity Analysis and Material Parameter Estimation
    of a Pre-Stressed Langevin Transducer.” <i>2025 International Congress on Ultrasonics</i>,
    AMA Service GmbH, 2025, pp. 138–141, doi:<a href="https://doi.org/10.5162/ultrasonic2025/a18-a4">10.5162/ultrasonic2025/a18-a4</a>.
  short: 'O. Friesen, C. Scheidemann, L. Claes, T. Hemsel, B. Henning, in: 2025 International
    Congress on Ultrasonics, AMA Service GmbH, Paderborn, 2025, pp. 138–141.'
date_created: 2025-11-25T12:23:06Z
date_updated: 2026-01-05T08:00:48Z
department:
- _id: '49'
- _id: '151'
doi: 10.5162/ultrasonic2025/a18-a4
language:
- iso: eng
page: 138–141
place: Paderborn
project:
- _id: '245'
  name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken
    für Leistungsschallanwendungen (NEPTUN)'
publication: 2025 International Congress on Ultrasonics
publisher: AMA Service GmbH
status: public
title: Sensitivity Analysis and Material Parameter Estimation of a Pre-Stressed Langevin
  Transducer
type: conference
user_id: '11829'
year: '2025'
...
---
_id: '62298'
author:
- first_name: Raphael
  full_name: Kuess, Raphael
  last_name: Kuess
- first_name: Olga
  full_name: Friesen, Olga
  id: '44026'
  last_name: Friesen
- first_name: Bernd
  full_name: Henning, Bernd
  id: '213'
  last_name: Henning
- first_name: Andrea
  full_name: Walther, Andrea
  last_name: Walther
citation:
  ama: 'Kuess R, Friesen O, Henning B, Walther A. Identification of temperature-dependent
    material parameter functions in piezoelectricity. In: <i>2025 International Congress
    on Ultrasonics</i>. AMA Service GmbH; 2025:134–137. doi:<a href="https://doi.org/10.5162/ultrasonic2025/a18-a3">10.5162/ultrasonic2025/a18-a3</a>'
  apa: Kuess, R., Friesen, O., Henning, B., &#38; Walther, A. (2025). Identification
    of temperature-dependent material parameter functions in piezoelectricity. <i>2025
    International Congress on Ultrasonics</i>, 134–137. <a href="https://doi.org/10.5162/ultrasonic2025/a18-a3">https://doi.org/10.5162/ultrasonic2025/a18-a3</a>
  bibtex: '@inproceedings{Kuess_Friesen_Henning_Walther_2025, place={Germany}, title={Identification
    of temperature-dependent material parameter functions in piezoelectricity}, DOI={<a
    href="https://doi.org/10.5162/ultrasonic2025/a18-a3">10.5162/ultrasonic2025/a18-a3</a>},
    booktitle={2025 International Congress on Ultrasonics}, publisher={AMA Service
    GmbH}, author={Kuess, Raphael and Friesen, Olga and Henning, Bernd and Walther,
    Andrea}, year={2025}, pages={134–137} }'
  chicago: 'Kuess, Raphael, Olga Friesen, Bernd Henning, and Andrea Walther. “Identification
    of Temperature-Dependent Material Parameter Functions in Piezoelectricity.” In
    <i>2025 International Congress on Ultrasonics</i>, 134–137. Germany: AMA Service
    GmbH, 2025. <a href="https://doi.org/10.5162/ultrasonic2025/a18-a3">https://doi.org/10.5162/ultrasonic2025/a18-a3</a>.'
  ieee: 'R. Kuess, O. Friesen, B. Henning, and A. Walther, “Identification of temperature-dependent
    material parameter functions in piezoelectricity,” in <i>2025 International Congress
    on Ultrasonics</i>, 2025, pp. 134–137, doi: <a href="https://doi.org/10.5162/ultrasonic2025/a18-a3">10.5162/ultrasonic2025/a18-a3</a>.'
  mla: Kuess, Raphael, et al. “Identification of Temperature-Dependent Material Parameter
    Functions in Piezoelectricity.” <i>2025 International Congress on Ultrasonics</i>,
    AMA Service GmbH, 2025, pp. 134–137, doi:<a href="https://doi.org/10.5162/ultrasonic2025/a18-a3">10.5162/ultrasonic2025/a18-a3</a>.
  short: 'R. Kuess, O. Friesen, B. Henning, A. Walther, in: 2025 International Congress
    on Ultrasonics, AMA Service GmbH, Germany, 2025, pp. 134–137.'
date_created: 2025-11-25T12:23:06Z
date_updated: 2026-01-05T08:01:47Z
department:
- _id: '49'
doi: 10.5162/ultrasonic2025/a18-a3
language:
- iso: eng
page: 134–137
place: Germany
project:
- _id: '245'
  name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken
    für Leistungsschallanwendungen (NEPTUN)'
publication: 2025 International Congress on Ultrasonics
publisher: AMA Service GmbH
status: public
title: Identification of temperature-dependent material parameter functions in piezoelectricity
type: conference
user_id: '11829'
year: '2025'
...
---
_id: '59689'
author:
- first_name: Olga
  full_name: Friesen, Olga
  id: '44026'
  last_name: Friesen
- first_name: Lars
  full_name: Meihost, Lars
  id: '24769'
  last_name: Meihost
- first_name: Kevin
  full_name: Koch, Kevin
  last_name: Koch
- first_name: Leander
  full_name: Claes, Leander
  id: '11829'
  last_name: Claes
  orcid: 0000-0002-4393-268X
- first_name: Bernd
  full_name: Henning, Bernd
  id: '213'
  last_name: Henning
citation:
  ama: 'Friesen O, Meihost L, Koch K, Claes L, Henning B. Estimation of piezoelectric
    material parameters under varying electric field conditions. In: ; 2025. doi:<a
    href="https://doi.org/10.71568/DASDAGA2025.078">10.71568/DASDAGA2025.078</a>'
  apa: Friesen, O., Meihost, L., Koch, K., Claes, L., &#38; Henning, B. (2025). <i>Estimation
    of piezoelectric material parameters under varying electric field conditions</i>.
    DAS | DAGA 2025 - 51st Annual Meeting on Acoustics, Copenhagen. <a href="https://doi.org/10.71568/DASDAGA2025.078">https://doi.org/10.71568/DASDAGA2025.078</a>
  bibtex: '@inproceedings{Friesen_Meihost_Koch_Claes_Henning_2025, title={Estimation
    of piezoelectric material parameters under varying electric field conditions},
    DOI={<a href="https://doi.org/10.71568/DASDAGA2025.078">10.71568/DASDAGA2025.078</a>},
    author={Friesen, Olga and Meihost, Lars and Koch, Kevin and Claes, Leander and
    Henning, Bernd}, year={2025} }'
  chicago: Friesen, Olga, Lars Meihost, Kevin Koch, Leander Claes, and Bernd Henning.
    “Estimation of Piezoelectric Material Parameters under Varying Electric Field
    Conditions,” 2025. <a href="https://doi.org/10.71568/DASDAGA2025.078">https://doi.org/10.71568/DASDAGA2025.078</a>.
  ieee: 'O. Friesen, L. Meihost, K. Koch, L. Claes, and B. Henning, “Estimation of
    piezoelectric material parameters under varying electric field conditions,” presented
    at the DAS | DAGA 2025 - 51st Annual Meeting on Acoustics, Copenhagen, 2025, doi:
    <a href="https://doi.org/10.71568/DASDAGA2025.078">10.71568/DASDAGA2025.078</a>.'
  mla: Friesen, Olga, et al. <i>Estimation of Piezoelectric Material Parameters under
    Varying Electric Field Conditions</i>. 2025, doi:<a href="https://doi.org/10.71568/DASDAGA2025.078">10.71568/DASDAGA2025.078</a>.
  short: 'O. Friesen, L. Meihost, K. Koch, L. Claes, B. Henning, in: 2025.'
conference:
  end_date: 2025-03-20
  location: Copenhagen
  name: DAS | DAGA 2025 - 51st Annual Meeting on Acoustics
  start_date: 2025-03-17
date_created: 2025-04-25T08:51:32Z
date_updated: 2026-01-05T08:02:20Z
department:
- _id: '49'
doi: 10.71568/DASDAGA2025.078
language:
- iso: eng
main_file_link:
- open_access: '1'
oa: '1'
project:
- _id: '52'
  name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
- _id: '245'
  name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken
    für Leistungsschallanwendungen (NEPTUN)'
status: public
title: Estimation of piezoelectric material parameters under varying electric field
  conditions
type: conference
user_id: '11829'
year: '2025'
...
---
_id: '63250'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n                  <jats:p>\r\n                    An
    initial-boundary value problem for\r\n                    <jats:disp-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$\\begin{aligned}
    \\left\\{ \\begin{array}{ll}u_{tt} = \\big (\\gamma (\\Theta ) u_{xt}\\big )_x
    + au_{xx} - \\big (f(\\Theta )\\big )_x, \\qquad &amp;  x\\in \\Omega , \\ t&gt;0,
    \\\\[1mm] \\Theta _t = \\Theta _{xx} + \\gamma (\\Theta ) u_{xt}^2 - f(\\Theta
    ) u_{xt}, \\qquad &amp;  x\\in \\Omega , \\ t&gt;0, \\end{array} \\right. \\end{aligned}$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mtable>\r\n
    \                             <mml:mtr>\r\n                                <mml:mtd>\r\n
    \                                 <mml:mfenced>\r\n                                    <mml:mrow>\r\n
    \                                     <mml:mtable>\r\n                                        <mml:mtr>\r\n
    \                                         <mml:mtd>\r\n                                            <mml:mrow>\r\n
    \                                             <mml:msub>\r\n                                                <mml:mi>u</mml:mi>\r\n
    \                                               <mml:mrow>\r\n                                                  <mml:mi>tt</mml:mi>\r\n
    \                                               </mml:mrow>\r\n                                              </mml:msub>\r\n
    \                                             <mml:mo>=</mml:mo>\r\n                                              <mml:mrow>\r\n
    \                                               <mml:mo>(</mml:mo>\r\n                                              </mml:mrow>\r\n
    \                                             <mml:mi>γ</mml:mi>\r\n                                              <mml:mrow>\r\n
    \                                               <mml:mo>(</mml:mo>\r\n                                                <mml:mi>Θ</mml:mi>\r\n
    \                                               <mml:mo>)</mml:mo>\r\n                                              </mml:mrow>\r\n
    \                                             <mml:msub>\r\n                                                <mml:mi>u</mml:mi>\r\n
    \                                               <mml:mrow>\r\n                                                  <mml:mi>xt</mml:mi>\r\n
    \                                               </mml:mrow>\r\n                                              </mml:msub>\r\n
    \                                             <mml:msub>\r\n                                                <mml:mrow>\r\n
    \                                                 <mml:mo>)</mml:mo>\r\n                                                </mml:mrow>\r\n
    \                                               <mml:mi>x</mml:mi>\r\n                                              </mml:msub>\r\n
    \                                             <mml:mo>+</mml:mo>\r\n                                              <mml:mi>a</mml:mi>\r\n
    \                                             <mml:msub>\r\n                                                <mml:mi>u</mml:mi>\r\n
    \                                               <mml:mrow>\r\n                                                  <mml:mi>xx</mml:mi>\r\n
    \                                               </mml:mrow>\r\n                                              </mml:msub>\r\n
    \                                             <mml:mo>-</mml:mo>\r\n                                              <mml:mrow>\r\n
    \                                               <mml:mo>(</mml:mo>\r\n                                              </mml:mrow>\r\n
    \                                             <mml:mi>f</mml:mi>\r\n                                              <mml:mrow>\r\n
    \                                               <mml:mo>(</mml:mo>\r\n                                                <mml:mi>Θ</mml:mi>\r\n
    \                                               <mml:mo>)</mml:mo>\r\n                                              </mml:mrow>\r\n
    \                                             <mml:msub>\r\n                                                <mml:mrow>\r\n
    \                                                 <mml:mo>)</mml:mo>\r\n                                                </mml:mrow>\r\n
    \                                               <mml:mi>x</mml:mi>\r\n                                              </mml:msub>\r\n
    \                                             <mml:mo>,</mml:mo>\r\n                                              <mml:mspace/>\r\n
    \                                           </mml:mrow>\r\n                                          </mml:mtd>\r\n
    \                                         <mml:mtd>\r\n                                            <mml:mrow>\r\n
    \                                             <mml:mi>x</mml:mi>\r\n                                              <mml:mo>∈</mml:mo>\r\n
    \                                             <mml:mi>Ω</mml:mi>\r\n                                              <mml:mo>,</mml:mo>\r\n
    \                                             <mml:mspace/>\r\n                                              <mml:mi>t</mml:mi>\r\n
    \                                             <mml:mo>&gt;</mml:mo>\r\n                                              <mml:mn>0</mml:mn>\r\n
    \                                             <mml:mo>,</mml:mo>\r\n                                            </mml:mrow>\r\n
    \                                         </mml:mtd>\r\n                                        </mml:mtr>\r\n
    \                                       <mml:mtr>\r\n                                          <mml:mtd>\r\n
    \                                           <mml:mrow>\r\n                                              <mml:mrow/>\r\n
    \                                             <mml:mrow>\r\n                                                <mml:mo>[</mml:mo>\r\n
    \                                               <mml:mn>1</mml:mn>\r\n                                                <mml:mi>m</mml:mi>\r\n
    \                                               <mml:mi>m</mml:mi>\r\n                                                <mml:mo>]</mml:mo>\r\n
    \                                             </mml:mrow>\r\n                                              <mml:msub>\r\n
    \                                               <mml:mi>Θ</mml:mi>\r\n                                                <mml:mi>t</mml:mi>\r\n
    \                                             </mml:msub>\r\n                                              <mml:mo>=</mml:mo>\r\n
    \                                             <mml:msub>\r\n                                                <mml:mi>Θ</mml:mi>\r\n
    \                                               <mml:mrow>\r\n                                                  <mml:mi>xx</mml:mi>\r\n
    \                                               </mml:mrow>\r\n                                              </mml:msub>\r\n
    \                                             <mml:mo>+</mml:mo>\r\n                                              <mml:mi>γ</mml:mi>\r\n
    \                                             <mml:mrow>\r\n                                                <mml:mo>(</mml:mo>\r\n
    \                                               <mml:mi>Θ</mml:mi>\r\n                                                <mml:mo>)</mml:mo>\r\n
    \                                             </mml:mrow>\r\n                                              <mml:msubsup>\r\n
    \                                               <mml:mi>u</mml:mi>\r\n                                                <mml:mrow>\r\n
    \                                                 <mml:mi>xt</mml:mi>\r\n                                                </mml:mrow>\r\n
    \                                               <mml:mn>2</mml:mn>\r\n                                              </mml:msubsup>\r\n
    \                                             <mml:mo>-</mml:mo>\r\n                                              <mml:mi>f</mml:mi>\r\n
    \                                             <mml:mrow>\r\n                                                <mml:mo>(</mml:mo>\r\n
    \                                               <mml:mi>Θ</mml:mi>\r\n                                                <mml:mo>)</mml:mo>\r\n
    \                                             </mml:mrow>\r\n                                              <mml:msub>\r\n
    \                                               <mml:mi>u</mml:mi>\r\n                                                <mml:mrow>\r\n
    \                                                 <mml:mi>xt</mml:mi>\r\n                                                </mml:mrow>\r\n
    \                                             </mml:msub>\r\n                                              <mml:mo>,</mml:mo>\r\n
    \                                             <mml:mspace/>\r\n                                            </mml:mrow>\r\n
    \                                         </mml:mtd>\r\n                                          <mml:mtd>\r\n
    \                                           <mml:mrow>\r\n                                              <mml:mi>x</mml:mi>\r\n
    \                                             <mml:mo>∈</mml:mo>\r\n                                              <mml:mi>Ω</mml:mi>\r\n
    \                                             <mml:mo>,</mml:mo>\r\n                                              <mml:mspace/>\r\n
    \                                             <mml:mi>t</mml:mi>\r\n                                              <mml:mo>&gt;</mml:mo>\r\n
    \                                             <mml:mn>0</mml:mn>\r\n                                              <mml:mo>,</mml:mo>\r\n
    \                                           </mml:mrow>\r\n                                          </mml:mtd>\r\n
    \                                       </mml:mtr>\r\n                                      </mml:mtable>\r\n
    \                                   </mml:mrow>\r\n                                  </mml:mfenced>\r\n
    \                               </mml:mtd>\r\n                              </mml:mtr>\r\n
    \                           </mml:mtable>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:disp-formula>\r\n                    is considered
    in an open bounded real interval\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$\\Omega
    $$</jats:tex-math>\r\n                        <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mi>Ω</mml:mi>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   . Under the assumption that\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$\\gamma
    \\in C^0([0,\\infty ))$$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:mi>γ</mml:mi>\r\n                            <mml:mo>∈</mml:mo>\r\n
    \                           <mml:msup>\r\n                              <mml:mi>C</mml:mi>\r\n
    \                             <mml:mn>0</mml:mn>\r\n                            </mml:msup>\r\n
    \                           <mml:mrow>\r\n                              <mml:mo>(</mml:mo>\r\n
    \                             <mml:mrow>\r\n                                <mml:mo>[</mml:mo>\r\n
    \                               <mml:mn>0</mml:mn>\r\n                                <mml:mo>,</mml:mo>\r\n
    \                               <mml:mi>∞</mml:mi>\r\n                                <mml:mo>)</mml:mo>\r\n
    \                             </mml:mrow>\r\n                              <mml:mo>)</mml:mo>\r\n
    \                           </mml:mrow>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    and\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$f\\in
    C^0([0,\\infty ))$$</jats:tex-math>\r\n                        <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mi>f</mml:mi>\r\n
    \                           <mml:mo>∈</mml:mo>\r\n                            <mml:msup>\r\n
    \                             <mml:mi>C</mml:mi>\r\n                              <mml:mn>0</mml:mn>\r\n
    \                           </mml:msup>\r\n                            <mml:mrow>\r\n
    \                             <mml:mo>(</mml:mo>\r\n                              <mml:mrow>\r\n
    \                               <mml:mo>[</mml:mo>\r\n                                <mml:mn>0</mml:mn>\r\n
    \                               <mml:mo>,</mml:mo>\r\n                                <mml:mi>∞</mml:mi>\r\n
    \                               <mml:mo>)</mml:mo>\r\n                              </mml:mrow>\r\n
    \                             <mml:mo>)</mml:mo>\r\n                            </mml:mrow>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   are such that\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$f(0)=0$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mi>f</mml:mi>\r\n
    \                           <mml:mo>(</mml:mo>\r\n                            <mml:mn>0</mml:mn>\r\n
    \                           <mml:mo>)</mml:mo>\r\n                            <mml:mo>=</mml:mo>\r\n
    \                           <mml:mn>0</mml:mn>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    , and\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$k_\\gamma
    \\le \\gamma \\le K_\\gamma $$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:msub>\r\n                              <mml:mi>k</mml:mi>\r\n
    \                             <mml:mi>γ</mml:mi>\r\n                            </mml:msub>\r\n
    \                           <mml:mo>≤</mml:mo>\r\n                            <mml:mi>γ</mml:mi>\r\n
    \                           <mml:mo>≤</mml:mo>\r\n                            <mml:msub>\r\n
    \                             <mml:mi>K</mml:mi>\r\n                              <mml:mi>γ</mml:mi>\r\n
    \                           </mml:msub>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    as well as\r\n
    \                   <jats:disp-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$\\begin{aligned} |f(\\xi )| \\le K_f
    \\cdot (\\xi +1)^\\alpha \\qquad \\hbox {for all } \\xi \\ge 0 \\end{aligned}$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mtable>\r\n
    \                             <mml:mtr>\r\n                                <mml:mtd>\r\n
    \                                 <mml:mrow>\r\n                                    <mml:mrow>\r\n
    \                                     <mml:mo>|</mml:mo>\r\n                                      <mml:mi>f</mml:mi>\r\n
    \                                     <mml:mrow>\r\n                                        <mml:mo>(</mml:mo>\r\n
    \                                       <mml:mi>ξ</mml:mi>\r\n                                        <mml:mo>)</mml:mo>\r\n
    \                                     </mml:mrow>\r\n                                      <mml:mo>|</mml:mo>\r\n
    \                                   </mml:mrow>\r\n                                    <mml:mo>≤</mml:mo>\r\n
    \                                   <mml:msub>\r\n                                      <mml:mi>K</mml:mi>\r\n
    \                                     <mml:mi>f</mml:mi>\r\n                                    </mml:msub>\r\n
    \                                   <mml:mo>·</mml:mo>\r\n                                    <mml:msup>\r\n
    \                                     <mml:mrow>\r\n                                        <mml:mo>(</mml:mo>\r\n
    \                                       <mml:mi>ξ</mml:mi>\r\n                                        <mml:mo>+</mml:mo>\r\n
    \                                       <mml:mn>1</mml:mn>\r\n                                        <mml:mo>)</mml:mo>\r\n
    \                                     </mml:mrow>\r\n                                      <mml:mi>α</mml:mi>\r\n
    \                                   </mml:msup>\r\n                                    <mml:mspace/>\r\n
    \                                   <mml:mtext>for all</mml:mtext>\r\n                                    <mml:mspace/>\r\n
    \                                   <mml:mi>ξ</mml:mi>\r\n                                    <mml:mo>≥</mml:mo>\r\n
    \                                   <mml:mn>0</mml:mn>\r\n                                  </mml:mrow>\r\n
    \                               </mml:mtd>\r\n                              </mml:mtr>\r\n
    \                           </mml:mtable>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:disp-formula>\r\n                    with some\r\n
    \                   <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$k_\\gamma&gt;0, K_\\gamma&gt;0, K_f&gt;0$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:msub>\r\n
    \                             <mml:mi>k</mml:mi>\r\n                              <mml:mi>γ</mml:mi>\r\n
    \                           </mml:msub>\r\n                            <mml:mo>&gt;</mml:mo>\r\n
    \                           <mml:mn>0</mml:mn>\r\n                            <mml:mo>,</mml:mo>\r\n
    \                           <mml:msub>\r\n                              <mml:mi>K</mml:mi>\r\n
    \                             <mml:mi>γ</mml:mi>\r\n                            </mml:msub>\r\n
    \                           <mml:mo>&gt;</mml:mo>\r\n                            <mml:mn>0</mml:mn>\r\n
    \                           <mml:mo>,</mml:mo>\r\n                            <mml:msub>\r\n
    \                             <mml:mi>K</mml:mi>\r\n                              <mml:mi>f</mml:mi>\r\n
    \                           </mml:msub>\r\n                            <mml:mo>&gt;</mml:mo>\r\n
    \                           <mml:mn>0</mml:mn>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    and\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$\\alpha
    &lt;\\frac{3}{2}$$</jats:tex-math>\r\n                        <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mi>α</mml:mi>\r\n
    \                           <mml:mo>&lt;</mml:mo>\r\n                            <mml:mfrac>\r\n
    \                             <mml:mn>3</mml:mn>\r\n                              <mml:mn>2</mml:mn>\r\n
    \                           </mml:mfrac>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    , for all suitably
    regular initial data of arbitrary size a statement on global existence of a global
    weak solution is derived. By particularly covering the thermodynamically consistent
    choice\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$f\\equiv id$$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:mi>f</mml:mi>\r\n                            <mml:mo>≡</mml:mo>\r\n
    \                           <mml:mi>i</mml:mi>\r\n                            <mml:mi>d</mml:mi>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   of predominant physical relevance, this appears to go beyond
    previous related literature which seems to either rely on independence of\r\n
    \                   <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$\\gamma $$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mi>γ</mml:mi>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    on\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$\\Theta
    $$</jats:tex-math>\r\n                        <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mi>Θ</mml:mi>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   , or to operate on finite time intervals.\r\n                  </jats:p>"
article_number: '192'
author:
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Winkler M. Large-data solutions in one-dimensional thermoviscoelasticity involving
    temperature-dependent viscosities. <i>Zeitschrift für angewandte Mathematik und
    Physik</i>. 2025;76(5). doi:<a href="https://doi.org/10.1007/s00033-025-02582-y">10.1007/s00033-025-02582-y</a>
  apa: Winkler, M. (2025). Large-data solutions in one-dimensional thermoviscoelasticity
    involving temperature-dependent viscosities. <i>Zeitschrift Für Angewandte Mathematik
    Und Physik</i>, <i>76</i>(5), Article 192. <a href="https://doi.org/10.1007/s00033-025-02582-y">https://doi.org/10.1007/s00033-025-02582-y</a>
  bibtex: '@article{Winkler_2025, title={Large-data solutions in one-dimensional thermoviscoelasticity
    involving temperature-dependent viscosities}, volume={76}, DOI={<a href="https://doi.org/10.1007/s00033-025-02582-y">10.1007/s00033-025-02582-y</a>},
    number={5192}, journal={Zeitschrift für angewandte Mathematik und Physik}, publisher={Springer
    Science and Business Media LLC}, author={Winkler, Michael}, year={2025} }'
  chicago: Winkler, Michael. “Large-Data Solutions in One-Dimensional Thermoviscoelasticity
    Involving Temperature-Dependent Viscosities.” <i>Zeitschrift Für Angewandte Mathematik
    Und Physik</i> 76, no. 5 (2025). <a href="https://doi.org/10.1007/s00033-025-02582-y">https://doi.org/10.1007/s00033-025-02582-y</a>.
  ieee: 'M. Winkler, “Large-data solutions in one-dimensional thermoviscoelasticity
    involving temperature-dependent viscosities,” <i>Zeitschrift für angewandte Mathematik
    und Physik</i>, vol. 76, no. 5, Art. no. 192, 2025, doi: <a href="https://doi.org/10.1007/s00033-025-02582-y">10.1007/s00033-025-02582-y</a>.'
  mla: Winkler, Michael. “Large-Data Solutions in One-Dimensional Thermoviscoelasticity
    Involving Temperature-Dependent Viscosities.” <i>Zeitschrift Für Angewandte Mathematik
    Und Physik</i>, vol. 76, no. 5, 192, Springer Science and Business Media LLC,
    2025, doi:<a href="https://doi.org/10.1007/s00033-025-02582-y">10.1007/s00033-025-02582-y</a>.
  short: M. Winkler, Zeitschrift Für Angewandte Mathematik Und Physik 76 (2025).
date_created: 2025-12-18T19:03:19Z
date_updated: 2026-04-23T12:20:44Z
doi: 10.1007/s00033-025-02582-y
intvolume: '        76'
issue: '5'
language:
- iso: eng
project:
- _id: '245'
  name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken
    für Leistungsschallanwendungen (NEPTUN)'
publication: Zeitschrift für angewandte Mathematik und Physik
publication_identifier:
  issn:
  - 0044-2275
  - 1420-9039
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Large-data solutions in one-dimensional thermoviscoelasticity involving temperature-dependent
  viscosities
type: journal_article
user_id: '31496'
volume: 76
year: '2025'
...
---
_id: '63249'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n                  <jats:p>\r\n                    The
    model\r\n                    <jats:disp-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$\\begin{aligned} \\left\\{ \\begin{array}{l}u_{tt}
    = \\big (\\gamma (\\Theta ) u_{xt}\\big )_x + au_{xx} - \\big (f(\\Theta )\\big
    )_x, \\\\[1mm] \\Theta _t = \\Theta _{xx} + \\gamma (\\Theta ) u_{xt}^2 - f(\\Theta
    ) u_{xt}, \\end{array} \\right. \\end{aligned}$$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:mtable>\r\n                              <mml:mtr>\r\n
    \                               <mml:mtd>\r\n                                  <mml:mfenced>\r\n
    \                                   <mml:mrow>\r\n                                      <mml:mtable>\r\n
    \                                       <mml:mtr>\r\n                                          <mml:mtd>\r\n
    \                                           <mml:mrow>\r\n                                              <mml:msub>\r\n
    \                                               <mml:mi>u</mml:mi>\r\n                                                <mml:mrow>\r\n
    \                                                 <mml:mi>tt</mml:mi>\r\n                                                </mml:mrow>\r\n
    \                                             </mml:msub>\r\n                                              <mml:mo>=</mml:mo>\r\n
    \                                             <mml:mrow>\r\n                                                <mml:mo>(</mml:mo>\r\n
    \                                             </mml:mrow>\r\n                                              <mml:mi>γ</mml:mi>\r\n
    \                                             <mml:mrow>\r\n                                                <mml:mo>(</mml:mo>\r\n
    \                                               <mml:mi>Θ</mml:mi>\r\n                                                <mml:mo>)</mml:mo>\r\n
    \                                             </mml:mrow>\r\n                                              <mml:msub>\r\n
    \                                               <mml:mi>u</mml:mi>\r\n                                                <mml:mrow>\r\n
    \                                                 <mml:mi>xt</mml:mi>\r\n                                                </mml:mrow>\r\n
    \                                             </mml:msub>\r\n                                              <mml:msub>\r\n
    \                                               <mml:mrow>\r\n                                                  <mml:mo>)</mml:mo>\r\n
    \                                               </mml:mrow>\r\n                                                <mml:mi>x</mml:mi>\r\n
    \                                             </mml:msub>\r\n                                              <mml:mo>+</mml:mo>\r\n
    \                                             <mml:mi>a</mml:mi>\r\n                                              <mml:msub>\r\n
    \                                               <mml:mi>u</mml:mi>\r\n                                                <mml:mrow>\r\n
    \                                                 <mml:mi>xx</mml:mi>\r\n                                                </mml:mrow>\r\n
    \                                             </mml:msub>\r\n                                              <mml:mo>-</mml:mo>\r\n
    \                                             <mml:mrow>\r\n                                                <mml:mo>(</mml:mo>\r\n
    \                                             </mml:mrow>\r\n                                              <mml:mi>f</mml:mi>\r\n
    \                                             <mml:mrow>\r\n                                                <mml:mo>(</mml:mo>\r\n
    \                                               <mml:mi>Θ</mml:mi>\r\n                                                <mml:mo>)</mml:mo>\r\n
    \                                             </mml:mrow>\r\n                                              <mml:msub>\r\n
    \                                               <mml:mrow>\r\n                                                  <mml:mo>)</mml:mo>\r\n
    \                                               </mml:mrow>\r\n                                                <mml:mi>x</mml:mi>\r\n
    \                                             </mml:msub>\r\n                                              <mml:mo>,</mml:mo>\r\n
    \                                           </mml:mrow>\r\n                                          </mml:mtd>\r\n
    \                                       </mml:mtr>\r\n                                        <mml:mtr>\r\n
    \                                         <mml:mtd>\r\n                                            <mml:mrow>\r\n
    \                                             <mml:mrow/>\r\n                                              <mml:mrow>\r\n
    \                                               <mml:mo>[</mml:mo>\r\n                                                <mml:mn>1</mml:mn>\r\n
    \                                               <mml:mi>m</mml:mi>\r\n                                                <mml:mi>m</mml:mi>\r\n
    \                                               <mml:mo>]</mml:mo>\r\n                                              </mml:mrow>\r\n
    \                                             <mml:msub>\r\n                                                <mml:mi>Θ</mml:mi>\r\n
    \                                               <mml:mi>t</mml:mi>\r\n                                              </mml:msub>\r\n
    \                                             <mml:mo>=</mml:mo>\r\n                                              <mml:msub>\r\n
    \                                               <mml:mi>Θ</mml:mi>\r\n                                                <mml:mrow>\r\n
    \                                                 <mml:mi>xx</mml:mi>\r\n                                                </mml:mrow>\r\n
    \                                             </mml:msub>\r\n                                              <mml:mo>+</mml:mo>\r\n
    \                                             <mml:mi>γ</mml:mi>\r\n                                              <mml:mrow>\r\n
    \                                               <mml:mo>(</mml:mo>\r\n                                                <mml:mi>Θ</mml:mi>\r\n
    \                                               <mml:mo>)</mml:mo>\r\n                                              </mml:mrow>\r\n
    \                                             <mml:msubsup>\r\n                                                <mml:mi>u</mml:mi>\r\n
    \                                               <mml:mrow>\r\n                                                  <mml:mi>xt</mml:mi>\r\n
    \                                               </mml:mrow>\r\n                                                <mml:mn>2</mml:mn>\r\n
    \                                             </mml:msubsup>\r\n                                              <mml:mo>-</mml:mo>\r\n
    \                                             <mml:mi>f</mml:mi>\r\n                                              <mml:mrow>\r\n
    \                                               <mml:mo>(</mml:mo>\r\n                                                <mml:mi>Θ</mml:mi>\r\n
    \                                               <mml:mo>)</mml:mo>\r\n                                              </mml:mrow>\r\n
    \                                             <mml:msub>\r\n                                                <mml:mi>u</mml:mi>\r\n
    \                                               <mml:mrow>\r\n                                                  <mml:mi>xt</mml:mi>\r\n
    \                                               </mml:mrow>\r\n                                              </mml:msub>\r\n
    \                                             <mml:mo>,</mml:mo>\r\n                                            </mml:mrow>\r\n
    \                                         </mml:mtd>\r\n                                        </mml:mtr>\r\n
    \                                     </mml:mtable>\r\n                                    </mml:mrow>\r\n
    \                                 </mml:mfenced>\r\n                                </mml:mtd>\r\n
    \                             </mml:mtr>\r\n                            </mml:mtable>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:disp-formula>\r\n
    \                   for thermoviscoelastic evolution in one-dimensional Kelvin–Voigt
    materials is considered. By means of an approach based on maximal Sobolev regularity
    theory of scalar parabolic equations, it is shown that if\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$\\gamma
    _0&gt;0$$</jats:tex-math>\r\n                        <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:msub>\r\n
    \                             <mml:mi>γ</mml:mi>\r\n                              <mml:mn>0</mml:mn>\r\n
    \                           </mml:msub>\r\n                            <mml:mo>&gt;</mml:mo>\r\n
    \                           <mml:mn>0</mml:mn>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    is fixed, then
    there exists\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$\\delta =\\delta (\\gamma _0)&gt;0$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mi>δ</mml:mi>\r\n
    \                           <mml:mo>=</mml:mo>\r\n                            <mml:mi>δ</mml:mi>\r\n
    \                           <mml:mo>(</mml:mo>\r\n                            <mml:msub>\r\n
    \                             <mml:mi>γ</mml:mi>\r\n                              <mml:mn>0</mml:mn>\r\n
    \                           </mml:msub>\r\n                            <mml:mo>)</mml:mo>\r\n
    \                           <mml:mo>&gt;</mml:mo>\r\n                            <mml:mn>0</mml:mn>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   with the property that for suitably regular initial data of
    arbitrary size an associated initial boundary value problem posed in an open bounded
    interval admits a global classical solution whenever\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$\\gamma
    \\in C^2([0,\\infty ))$$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:mi>γ</mml:mi>\r\n                            <mml:mo>∈</mml:mo>\r\n
    \                           <mml:msup>\r\n                              <mml:mi>C</mml:mi>\r\n
    \                             <mml:mn>2</mml:mn>\r\n                            </mml:msup>\r\n
    \                           <mml:mrow>\r\n                              <mml:mo>(</mml:mo>\r\n
    \                             <mml:mrow>\r\n                                <mml:mo>[</mml:mo>\r\n
    \                               <mml:mn>0</mml:mn>\r\n                                <mml:mo>,</mml:mo>\r\n
    \                               <mml:mi>∞</mml:mi>\r\n                                <mml:mo>)</mml:mo>\r\n
    \                             </mml:mrow>\r\n                              <mml:mo>)</mml:mo>\r\n
    \                           </mml:mrow>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    and\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$f\\in
    C^2([0,\\infty ))$$</jats:tex-math>\r\n                        <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mi>f</mml:mi>\r\n
    \                           <mml:mo>∈</mml:mo>\r\n                            <mml:msup>\r\n
    \                             <mml:mi>C</mml:mi>\r\n                              <mml:mn>2</mml:mn>\r\n
    \                           </mml:msup>\r\n                            <mml:mrow>\r\n
    \                             <mml:mo>(</mml:mo>\r\n                              <mml:mrow>\r\n
    \                               <mml:mo>[</mml:mo>\r\n                                <mml:mn>0</mml:mn>\r\n
    \                               <mml:mo>,</mml:mo>\r\n                                <mml:mi>∞</mml:mi>\r\n
    \                               <mml:mo>)</mml:mo>\r\n                              </mml:mrow>\r\n
    \                             <mml:mo>)</mml:mo>\r\n                            </mml:mrow>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   are such that\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$f(0)=0$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mi>f</mml:mi>\r\n
    \                           <mml:mo>(</mml:mo>\r\n                            <mml:mn>0</mml:mn>\r\n
    \                           <mml:mo>)</mml:mo>\r\n                            <mml:mo>=</mml:mo>\r\n
    \                           <mml:mn>0</mml:mn>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    and\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$|f(\\xi
    )| \\le K_f \\cdot (\\xi +1)^\\alpha $$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:mrow>\r\n                              <mml:mo>|</mml:mo>\r\n
    \                             <mml:mi>f</mml:mi>\r\n                              <mml:mrow>\r\n
    \                               <mml:mo>(</mml:mo>\r\n                                <mml:mi>ξ</mml:mi>\r\n
    \                               <mml:mo>)</mml:mo>\r\n                              </mml:mrow>\r\n
    \                             <mml:mo>|</mml:mo>\r\n                            </mml:mrow>\r\n
    \                           <mml:mo>≤</mml:mo>\r\n                            <mml:msub>\r\n
    \                             <mml:mi>K</mml:mi>\r\n                              <mml:mi>f</mml:mi>\r\n
    \                           </mml:msub>\r\n                            <mml:mo>·</mml:mo>\r\n
    \                           <mml:msup>\r\n                              <mml:mrow>\r\n
    \                               <mml:mo>(</mml:mo>\r\n                                <mml:mi>ξ</mml:mi>\r\n
    \                               <mml:mo>+</mml:mo>\r\n                                <mml:mn>1</mml:mn>\r\n
    \                               <mml:mo>)</mml:mo>\r\n                              </mml:mrow>\r\n
    \                             <mml:mi>α</mml:mi>\r\n                            </mml:msup>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   for all\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$\\xi \\ge 0$$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:mi>ξ</mml:mi>\r\n                            <mml:mo>≥</mml:mo>\r\n
    \                           <mml:mn>0</mml:mn>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    and some\r\n
    \                   <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$K_f&gt;0$$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:msub>\r\n                              <mml:mi>K</mml:mi>\r\n
    \                             <mml:mi>f</mml:mi>\r\n                            </mml:msub>\r\n
    \                           <mml:mo>&gt;</mml:mo>\r\n                            <mml:mn>0</mml:mn>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   and\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$\\alpha &lt;\\frac{3}{2}$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mi>α</mml:mi>\r\n
    \                           <mml:mo>&lt;</mml:mo>\r\n                            <mml:mfrac>\r\n
    \                             <mml:mn>3</mml:mn>\r\n                              <mml:mn>2</mml:mn>\r\n
    \                           </mml:mfrac>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    , and that\r\n
    \                   <jats:disp-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$\\begin{aligned} \\gamma _0 \\le \\gamma
    (\\xi ) \\le \\gamma _0 + \\delta \\qquad \\hbox {for all } \\xi \\ge 0. \\end{aligned}$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mtable>\r\n
    \                             <mml:mtr>\r\n                                <mml:mtd>\r\n
    \                                 <mml:mrow>\r\n                                    <mml:msub>\r\n
    \                                     <mml:mi>γ</mml:mi>\r\n                                      <mml:mn>0</mml:mn>\r\n
    \                                   </mml:msub>\r\n                                    <mml:mo>≤</mml:mo>\r\n
    \                                   <mml:mi>γ</mml:mi>\r\n                                    <mml:mrow>\r\n
    \                                     <mml:mo>(</mml:mo>\r\n                                      <mml:mi>ξ</mml:mi>\r\n
    \                                     <mml:mo>)</mml:mo>\r\n                                    </mml:mrow>\r\n
    \                                   <mml:mo>≤</mml:mo>\r\n                                    <mml:msub>\r\n
    \                                     <mml:mi>γ</mml:mi>\r\n                                      <mml:mn>0</mml:mn>\r\n
    \                                   </mml:msub>\r\n                                    <mml:mo>+</mml:mo>\r\n
    \                                   <mml:mi>δ</mml:mi>\r\n                                    <mml:mspace/>\r\n
    \                                   <mml:mtext>for all</mml:mtext>\r\n                                    <mml:mspace/>\r\n
    \                                   <mml:mi>ξ</mml:mi>\r\n                                    <mml:mo>≥</mml:mo>\r\n
    \                                   <mml:mn>0</mml:mn>\r\n                                    <mml:mo>.</mml:mo>\r\n
    \                                 </mml:mrow>\r\n                                </mml:mtd>\r\n
    \                             </mml:mtr>\r\n                            </mml:mtable>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:disp-formula>\r\n
    \                   This is supplemented by a statement on global existence of
    certain strong solutions, particularly continuous in both components, under weaker
    conditions on the initial data.\r\n                  </jats:p>"
article_number: '108'
author:
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Winkler M. Large-data regular solutions in a one-dimensional thermoviscoelastic
    evolution problem involving temperature-dependent viscosities. <i>Journal of Evolution
    Equations</i>. 2025;25(4). doi:<a href="https://doi.org/10.1007/s00028-025-01144-z">10.1007/s00028-025-01144-z</a>
  apa: Winkler, M. (2025). Large-data regular solutions in a one-dimensional thermoviscoelastic
    evolution problem involving temperature-dependent viscosities. <i>Journal of Evolution
    Equations</i>, <i>25</i>(4), Article 108. <a href="https://doi.org/10.1007/s00028-025-01144-z">https://doi.org/10.1007/s00028-025-01144-z</a>
  bibtex: '@article{Winkler_2025, title={Large-data regular solutions in a one-dimensional
    thermoviscoelastic evolution problem involving temperature-dependent viscosities},
    volume={25}, DOI={<a href="https://doi.org/10.1007/s00028-025-01144-z">10.1007/s00028-025-01144-z</a>},
    number={4108}, journal={Journal of Evolution Equations}, publisher={Springer Science
    and Business Media LLC}, author={Winkler, Michael}, year={2025} }'
  chicago: Winkler, Michael. “Large-Data Regular Solutions in a One-Dimensional Thermoviscoelastic
    Evolution Problem Involving Temperature-Dependent Viscosities.” <i>Journal of
    Evolution Equations</i> 25, no. 4 (2025). <a href="https://doi.org/10.1007/s00028-025-01144-z">https://doi.org/10.1007/s00028-025-01144-z</a>.
  ieee: 'M. Winkler, “Large-data regular solutions in a one-dimensional thermoviscoelastic
    evolution problem involving temperature-dependent viscosities,” <i>Journal of
    Evolution Equations</i>, vol. 25, no. 4, Art. no. 108, 2025, doi: <a href="https://doi.org/10.1007/s00028-025-01144-z">10.1007/s00028-025-01144-z</a>.'
  mla: Winkler, Michael. “Large-Data Regular Solutions in a One-Dimensional Thermoviscoelastic
    Evolution Problem Involving Temperature-Dependent Viscosities.” <i>Journal of
    Evolution Equations</i>, vol. 25, no. 4, 108, Springer Science and Business Media
    LLC, 2025, doi:<a href="https://doi.org/10.1007/s00028-025-01144-z">10.1007/s00028-025-01144-z</a>.
  short: M. Winkler, Journal of Evolution Equations 25 (2025).
date_created: 2025-12-18T19:02:51Z
date_updated: 2026-04-23T12:19:51Z
doi: 10.1007/s00028-025-01144-z
intvolume: '        25'
issue: '4'
language:
- iso: eng
project:
- _id: '245'
  name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken
    für Leistungsschallanwendungen (NEPTUN)'
publication: Journal of Evolution Equations
publication_identifier:
  issn:
  - 1424-3199
  - 1424-3202
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Large-data regular solutions in a one-dimensional thermoviscoelastic evolution
  problem involving temperature-dependent viscosities
type: journal_article
user_id: '31496'
volume: 25
year: '2025'
...
---
_id: '63246'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n                  <jats:p>\r\n                    The
    hyperbolic-parabolic model\r\n                    <jats:disp-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$\\begin{aligned} \\left\\{ \\begin{array}{ll}
    u_{tt} = u_{xx} - \\big (f(\\Theta )\\big )_x, \\qquad &amp;  x\\in \\Omega ,
    \\ t&gt;0, \\\\ \\Theta _t = \\Theta _{xx} - f(\\Theta ) u_{xt}, \\qquad &amp;
    \ x\\in \\Omega , \\ t&gt;0, \\end{array} \\right. \\end{aligned}$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mtable>\r\n
    \                             <mml:mtr>\r\n                                <mml:mtd>\r\n
    \                                 <mml:mfenced>\r\n                                    <mml:mrow>\r\n
    \                                     <mml:mtable>\r\n                                        <mml:mtr>\r\n
    \                                         <mml:mtd>\r\n                                            <mml:mrow>\r\n
    \                                             <mml:msub>\r\n                                                <mml:mi>u</mml:mi>\r\n
    \                                               <mml:mrow>\r\n                                                  <mml:mi>tt</mml:mi>\r\n
    \                                               </mml:mrow>\r\n                                              </mml:msub>\r\n
    \                                             <mml:mo>=</mml:mo>\r\n                                              <mml:msub>\r\n
    \                                               <mml:mi>u</mml:mi>\r\n                                                <mml:mrow>\r\n
    \                                                 <mml:mi>xx</mml:mi>\r\n                                                </mml:mrow>\r\n
    \                                             </mml:msub>\r\n                                              <mml:mo>-</mml:mo>\r\n
    \                                             <mml:mrow>\r\n                                                <mml:mo>(</mml:mo>\r\n
    \                                             </mml:mrow>\r\n                                              <mml:mi>f</mml:mi>\r\n
    \                                             <mml:mrow>\r\n                                                <mml:mo>(</mml:mo>\r\n
    \                                               <mml:mi>Θ</mml:mi>\r\n                                                <mml:mo>)</mml:mo>\r\n
    \                                             </mml:mrow>\r\n                                              <mml:msub>\r\n
    \                                               <mml:mrow>\r\n                                                  <mml:mo>)</mml:mo>\r\n
    \                                               </mml:mrow>\r\n                                                <mml:mi>x</mml:mi>\r\n
    \                                             </mml:msub>\r\n                                              <mml:mo>,</mml:mo>\r\n
    \                                             <mml:mspace/>\r\n                                            </mml:mrow>\r\n
    \                                         </mml:mtd>\r\n                                          <mml:mtd>\r\n
    \                                           <mml:mrow>\r\n                                              <mml:mi>x</mml:mi>\r\n
    \                                             <mml:mo>∈</mml:mo>\r\n                                              <mml:mi>Ω</mml:mi>\r\n
    \                                             <mml:mo>,</mml:mo>\r\n                                              <mml:mspace/>\r\n
    \                                             <mml:mi>t</mml:mi>\r\n                                              <mml:mo>&gt;</mml:mo>\r\n
    \                                             <mml:mn>0</mml:mn>\r\n                                              <mml:mo>,</mml:mo>\r\n
    \                                           </mml:mrow>\r\n                                          </mml:mtd>\r\n
    \                                       </mml:mtr>\r\n                                        <mml:mtr>\r\n
    \                                         <mml:mtd>\r\n                                            <mml:mrow>\r\n
    \                                             <mml:mrow/>\r\n                                              <mml:msub>\r\n
    \                                               <mml:mi>Θ</mml:mi>\r\n                                                <mml:mi>t</mml:mi>\r\n
    \                                             </mml:msub>\r\n                                              <mml:mo>=</mml:mo>\r\n
    \                                             <mml:msub>\r\n                                                <mml:mi>Θ</mml:mi>\r\n
    \                                               <mml:mrow>\r\n                                                  <mml:mi>xx</mml:mi>\r\n
    \                                               </mml:mrow>\r\n                                              </mml:msub>\r\n
    \                                             <mml:mo>-</mml:mo>\r\n                                              <mml:mi>f</mml:mi>\r\n
    \                                             <mml:mrow>\r\n                                                <mml:mo>(</mml:mo>\r\n
    \                                               <mml:mi>Θ</mml:mi>\r\n                                                <mml:mo>)</mml:mo>\r\n
    \                                             </mml:mrow>\r\n                                              <mml:msub>\r\n
    \                                               <mml:mi>u</mml:mi>\r\n                                                <mml:mrow>\r\n
    \                                                 <mml:mi>xt</mml:mi>\r\n                                                </mml:mrow>\r\n
    \                                             </mml:msub>\r\n                                              <mml:mo>,</mml:mo>\r\n
    \                                             <mml:mspace/>\r\n                                            </mml:mrow>\r\n
    \                                         </mml:mtd>\r\n                                          <mml:mtd>\r\n
    \                                           <mml:mrow>\r\n                                              <mml:mi>x</mml:mi>\r\n
    \                                             <mml:mo>∈</mml:mo>\r\n                                              <mml:mi>Ω</mml:mi>\r\n
    \                                             <mml:mo>,</mml:mo>\r\n                                              <mml:mspace/>\r\n
    \                                             <mml:mi>t</mml:mi>\r\n                                              <mml:mo>&gt;</mml:mo>\r\n
    \                                             <mml:mn>0</mml:mn>\r\n                                              <mml:mo>,</mml:mo>\r\n
    \                                           </mml:mrow>\r\n                                          </mml:mtd>\r\n
    \                                       </mml:mtr>\r\n                                      </mml:mtable>\r\n
    \                                   </mml:mrow>\r\n                                  </mml:mfenced>\r\n
    \                               </mml:mtd>\r\n                              </mml:mtr>\r\n
    \                           </mml:mtable>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:disp-formula>\r\n                    for the evolution
    of the displacement variable\r\n                    <jats:italic>u</jats:italic>\r\n
    \                   and the temperature\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$\\Theta
    \\ge 0$$</jats:tex-math>\r\n                        <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mi>Θ</mml:mi>\r\n
    \                           <mml:mo>≥</mml:mo>\r\n                            <mml:mn>0</mml:mn>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   during thermoelastic interaction in a one-dimensional bounded
    interval\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$\\Omega $$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mi>Ω</mml:mi>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    is considered.
    Whereas the literature has provided comprehensive results on global solutions
    for sufficiently regular initial data\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$(u_0,u_{0t},\\Theta
    _0)=(u,u_t,\\Theta )|_{t=0}$$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:mrow>\r\n                              <mml:mo>(</mml:mo>\r\n
    \                             <mml:msub>\r\n                                <mml:mi>u</mml:mi>\r\n
    \                               <mml:mn>0</mml:mn>\r\n                              </mml:msub>\r\n
    \                             <mml:mo>,</mml:mo>\r\n                              <mml:msub>\r\n
    \                               <mml:mi>u</mml:mi>\r\n                                <mml:mrow>\r\n
    \                                 <mml:mn>0</mml:mn>\r\n                                  <mml:mi>t</mml:mi>\r\n
    \                               </mml:mrow>\r\n                              </mml:msub>\r\n
    \                             <mml:mo>,</mml:mo>\r\n                              <mml:msub>\r\n
    \                               <mml:mi>Θ</mml:mi>\r\n                                <mml:mn>0</mml:mn>\r\n
    \                             </mml:msub>\r\n                              <mml:mo>)</mml:mo>\r\n
    \                           </mml:mrow>\r\n                            <mml:mo>=</mml:mo>\r\n
    \                           <mml:mrow>\r\n                              <mml:mo>(</mml:mo>\r\n
    \                             <mml:mi>u</mml:mi>\r\n                              <mml:mo>,</mml:mo>\r\n
    \                             <mml:msub>\r\n                                <mml:mi>u</mml:mi>\r\n
    \                               <mml:mi>t</mml:mi>\r\n                              </mml:msub>\r\n
    \                             <mml:mo>,</mml:mo>\r\n                              <mml:mi>Θ</mml:mi>\r\n
    \                             <mml:mo>)</mml:mo>\r\n                            </mml:mrow>\r\n
    \                           <mml:msub>\r\n                              <mml:mrow>\r\n
    \                               <mml:mo>|</mml:mo>\r\n                              </mml:mrow>\r\n
    \                             <mml:mrow>\r\n                                <mml:mi>t</mml:mi>\r\n
    \                               <mml:mo>=</mml:mo>\r\n                                <mml:mn>0</mml:mn>\r\n
    \                             </mml:mrow>\r\n                            </mml:msub>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   when\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$f\\equiv id$$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:mi>f</mml:mi>\r\n                            <mml:mo>≡</mml:mo>\r\n
    \                           <mml:mi>i</mml:mi>\r\n                            <mml:mi>d</mml:mi>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   , it seems to have remained open so far how far a solution
    theory can be built solely on the two fundamental physical principles of energy
    conservation and entropy nondecrease. The present manuscript addresses this by
    asserting global existence of weak solutions under assumptions which are energy-
    and entropy-minimal in the sense of allowing for any initial data\r\n                    <jats:inline-formula>\r\n
    \                     <jats:alternatives>\r\n                        <jats:tex-math>$$u_0\\in
    W_0^{1,2}(\\Omega )$$</jats:tex-math>\r\n                        <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:msub>\r\n
    \                             <mml:mi>u</mml:mi>\r\n                              <mml:mn>0</mml:mn>\r\n
    \                           </mml:msub>\r\n                            <mml:mo>∈</mml:mo>\r\n
    \                           <mml:msubsup>\r\n                              <mml:mi>W</mml:mi>\r\n
    \                             <mml:mn>0</mml:mn>\r\n                              <mml:mrow>\r\n
    \                               <mml:mn>1</mml:mn>\r\n                                <mml:mo>,</mml:mo>\r\n
    \                               <mml:mn>2</mml:mn>\r\n                              </mml:mrow>\r\n
    \                           </mml:msubsup>\r\n                            <mml:mrow>\r\n
    \                             <mml:mo>(</mml:mo>\r\n                              <mml:mi>Ω</mml:mi>\r\n
    \                             <mml:mo>)</mml:mo>\r\n                            </mml:mrow>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   ,\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$u_{0t} \\in L^2(\\Omega )$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:msub>\r\n
    \                             <mml:mi>u</mml:mi>\r\n                              <mml:mrow>\r\n
    \                               <mml:mn>0</mml:mn>\r\n                                <mml:mi>t</mml:mi>\r\n
    \                             </mml:mrow>\r\n                            </mml:msub>\r\n
    \                           <mml:mo>∈</mml:mo>\r\n                            <mml:msup>\r\n
    \                             <mml:mi>L</mml:mi>\r\n                              <mml:mn>2</mml:mn>\r\n
    \                           </mml:msup>\r\n                            <mml:mrow>\r\n
    \                             <mml:mo>(</mml:mo>\r\n                              <mml:mi>Ω</mml:mi>\r\n
    \                             <mml:mo>)</mml:mo>\r\n                            </mml:mrow>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   and\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$0\\le \\Theta _0\\in L^1(\\Omega )$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mn>0</mml:mn>\r\n
    \                           <mml:mo>≤</mml:mo>\r\n                            <mml:msub>\r\n
    \                             <mml:mi>Θ</mml:mi>\r\n                              <mml:mn>0</mml:mn>\r\n
    \                           </mml:msub>\r\n                            <mml:mo>∈</mml:mo>\r\n
    \                           <mml:msup>\r\n                              <mml:mi>L</mml:mi>\r\n
    \                             <mml:mn>1</mml:mn>\r\n                            </mml:msup>\r\n
    \                           <mml:mrow>\r\n                              <mml:mo>(</mml:mo>\r\n
    \                             <mml:mi>Ω</mml:mi>\r\n                              <mml:mo>)</mml:mo>\r\n
    \                           </mml:mrow>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    , and which
    apply to arbitrary\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$f\\in C^1([0,\\infty ))$$</jats:tex-math>\r\n
    \                       <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                         <mml:mrow>\r\n                            <mml:mi>f</mml:mi>\r\n
    \                           <mml:mo>∈</mml:mo>\r\n                            <mml:msup>\r\n
    \                             <mml:mi>C</mml:mi>\r\n                              <mml:mn>1</mml:mn>\r\n
    \                           </mml:msup>\r\n                            <mml:mrow>\r\n
    \                             <mml:mo>(</mml:mo>\r\n                              <mml:mrow>\r\n
    \                               <mml:mo>[</mml:mo>\r\n                                <mml:mn>0</mml:mn>\r\n
    \                               <mml:mo>,</mml:mo>\r\n                                <mml:mi>∞</mml:mi>\r\n
    \                               <mml:mo>)</mml:mo>\r\n                              </mml:mrow>\r\n
    \                             <mml:mo>)</mml:mo>\r\n                            </mml:mrow>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   with\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$f(0)=0$$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:mi>f</mml:mi>\r\n                            <mml:mo>(</mml:mo>\r\n
    \                           <mml:mn>0</mml:mn>\r\n                            <mml:mo>)</mml:mo>\r\n
    \                           <mml:mo>=</mml:mo>\r\n                            <mml:mn>0</mml:mn>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   and\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$f'&gt;0$$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:msup>\r\n                              <mml:mi>f</mml:mi>\r\n
    \                             <mml:mo>′</mml:mo>\r\n                            </mml:msup>\r\n
    \                           <mml:mo>&gt;</mml:mo>\r\n                            <mml:mn>0</mml:mn>\r\n
    \                         </mml:mrow>\r\n                        </mml:math>\r\n
    \                     </jats:alternatives>\r\n                    </jats:inline-formula>\r\n
    \                   on\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n
    \                       <jats:tex-math>$$[0,\\infty )$$</jats:tex-math>\r\n                        <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                          <mml:mrow>\r\n
    \                           <mml:mo>[</mml:mo>\r\n                            <mml:mn>0</mml:mn>\r\n
    \                           <mml:mo>,</mml:mo>\r\n                            <mml:mi>∞</mml:mi>\r\n
    \                           <mml:mo>)</mml:mo>\r\n                          </mml:mrow>\r\n
    \                       </mml:math>\r\n                      </jats:alternatives>\r\n
    \                   </jats:inline-formula>\r\n                    .\r\n                  </jats:p>"
article_number: '1'
author:
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Winkler M. Rough solutions in one-dimensional nonlinear thermoelasticity. <i>Calculus
    of Variations and Partial Differential Equations</i>. 2025;65(1). doi:<a href="https://doi.org/10.1007/s00526-025-03170-8">10.1007/s00526-025-03170-8</a>
  apa: Winkler, M. (2025). Rough solutions in one-dimensional nonlinear thermoelasticity.
    <i>Calculus of Variations and Partial Differential Equations</i>, <i>65</i>(1),
    Article 1. <a href="https://doi.org/10.1007/s00526-025-03170-8">https://doi.org/10.1007/s00526-025-03170-8</a>
  bibtex: '@article{Winkler_2025, title={Rough solutions in one-dimensional nonlinear
    thermoelasticity}, volume={65}, DOI={<a href="https://doi.org/10.1007/s00526-025-03170-8">10.1007/s00526-025-03170-8</a>},
    number={11}, journal={Calculus of Variations and Partial Differential Equations},
    publisher={Springer Science and Business Media LLC}, author={Winkler, Michael},
    year={2025} }'
  chicago: Winkler, Michael. “Rough Solutions in One-Dimensional Nonlinear Thermoelasticity.”
    <i>Calculus of Variations and Partial Differential Equations</i> 65, no. 1 (2025).
    <a href="https://doi.org/10.1007/s00526-025-03170-8">https://doi.org/10.1007/s00526-025-03170-8</a>.
  ieee: 'M. Winkler, “Rough solutions in one-dimensional nonlinear thermoelasticity,”
    <i>Calculus of Variations and Partial Differential Equations</i>, vol. 65, no.
    1, Art. no. 1, 2025, doi: <a href="https://doi.org/10.1007/s00526-025-03170-8">10.1007/s00526-025-03170-8</a>.'
  mla: Winkler, Michael. “Rough Solutions in One-Dimensional Nonlinear Thermoelasticity.”
    <i>Calculus of Variations and Partial Differential Equations</i>, vol. 65, no.
    1, 1, Springer Science and Business Media LLC, 2025, doi:<a href="https://doi.org/10.1007/s00526-025-03170-8">10.1007/s00526-025-03170-8</a>.
  short: M. Winkler, Calculus of Variations and Partial Differential Equations 65
    (2025).
date_created: 2025-12-18T19:01:02Z
date_updated: 2026-04-23T12:18:59Z
doi: 10.1007/s00526-025-03170-8
intvolume: '        65'
issue: '1'
language:
- iso: eng
project:
- _id: '245'
  name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken
    für Leistungsschallanwendungen (NEPTUN)'
publication: Calculus of Variations and Partial Differential Equations
publication_identifier:
  issn:
  - 0944-2669
  - 1432-0835
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Rough solutions in one-dimensional nonlinear thermoelasticity
type: journal_article
user_id: '31496'
volume: 65
year: '2025'
...
---
_id: '62297'
author:
- first_name: Jonas
  full_name: Hölscher, Jonas
  id: '73952'
  last_name: Hölscher
- first_name: Olga
  full_name: Friesen, Olga
  id: '44026'
  last_name: Friesen
  orcid: 0009-0007-5598-9484
- first_name: Leander
  full_name: Claes, Leander
  id: '11829'
  last_name: Claes
  orcid: 0000-0002-4393-268X
- first_name: Carsten
  full_name: Spieker, Carsten
  id: '67587'
  last_name: Spieker
- first_name: Jens
  full_name: Förstner, Jens
  id: '158'
  last_name: Förstner
  orcid: 0000-0001-7059-9862
- first_name: Bernd
  full_name: Henning, Bernd
  id: '213'
  last_name: Henning
citation:
  ama: 'Hölscher J, Friesen O, Claes L, Spieker C, Förstner J, Henning B. Multiscale
    thermo-piezoelectric simulations using the finite element method. In: <i>2025
    International Congress on Ultrasonics</i>. AMA Service GmbH; 2025:130–133. doi:<a
    href="https://doi.org/10.5162/ultrasonic2025/a18-a2">10.5162/ultrasonic2025/a18-a2</a>'
  apa: Hölscher, J., Friesen, O., Claes, L., Spieker, C., Förstner, J., &#38; Henning,
    B. (2025). Multiscale thermo-piezoelectric simulations using the finite element
    method. <i>2025 International Congress on Ultrasonics</i>, 130–133. <a href="https://doi.org/10.5162/ultrasonic2025/a18-a2">https://doi.org/10.5162/ultrasonic2025/a18-a2</a>
  bibtex: '@inproceedings{Hölscher_Friesen_Claes_Spieker_Förstner_Henning_2025, place={Paderborn},
    title={Multiscale thermo-piezoelectric simulations using the finite element method},
    DOI={<a href="https://doi.org/10.5162/ultrasonic2025/a18-a2">10.5162/ultrasonic2025/a18-a2</a>},
    booktitle={2025 International Congress on Ultrasonics}, publisher={AMA Service
    GmbH}, author={Hölscher, Jonas and Friesen, Olga and Claes, Leander and Spieker,
    Carsten and Förstner, Jens and Henning, Bernd}, year={2025}, pages={130–133} }'
  chicago: 'Hölscher, Jonas, Olga Friesen, Leander Claes, Carsten Spieker, Jens Förstner,
    and Bernd Henning. “Multiscale Thermo-Piezoelectric Simulations Using the Finite
    Element Method.” In <i>2025 International Congress on Ultrasonics</i>, 130–133.
    Paderborn: AMA Service GmbH, 2025. <a href="https://doi.org/10.5162/ultrasonic2025/a18-a2">https://doi.org/10.5162/ultrasonic2025/a18-a2</a>.'
  ieee: 'J. Hölscher, O. Friesen, L. Claes, C. Spieker, J. Förstner, and B. Henning,
    “Multiscale thermo-piezoelectric simulations using the finite element method,”
    in <i>2025 International Congress on Ultrasonics</i>, 2025, pp. 130–133, doi:
    <a href="https://doi.org/10.5162/ultrasonic2025/a18-a2">10.5162/ultrasonic2025/a18-a2</a>.'
  mla: Hölscher, Jonas, et al. “Multiscale Thermo-Piezoelectric Simulations Using
    the Finite Element Method.” <i>2025 International Congress on Ultrasonics</i>,
    AMA Service GmbH, 2025, pp. 130–133, doi:<a href="https://doi.org/10.5162/ultrasonic2025/a18-a2">10.5162/ultrasonic2025/a18-a2</a>.
  short: 'J. Hölscher, O. Friesen, L. Claes, C. Spieker, J. Förstner, B. Henning,
    in: 2025 International Congress on Ultrasonics, AMA Service GmbH, Paderborn, 2025,
    pp. 130–133.'
date_created: 2025-11-25T12:23:06Z
date_updated: 2026-06-08T17:55:35Z
department:
- _id: '49'
- _id: '61'
doi: 10.5162/ultrasonic2025/a18-a2
keyword:
- tet_topic_piezo
language:
- iso: eng
page: 130–133
place: Paderborn
project:
- _id: '245'
  name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken
    für Leistungsschallanwendungen (NEPTUN)'
publication: 2025 International Congress on Ultrasonics
publisher: AMA Service GmbH
status: public
title: Multiscale thermo-piezoelectric simulations using the finite element method
type: conference
user_id: '158'
year: '2025'
...
---
_id: '62296'
author:
- first_name: Carsten
  full_name: Spieker, Carsten
  id: '67587'
  last_name: Spieker
- first_name: Jens
  full_name: Förstner, Jens
  id: '158'
  last_name: Förstner
  orcid: 0000-0001-7059-9862
- first_name: Jonas
  full_name: Hölscher, Jonas
  id: '73952'
  last_name: Hölscher
- first_name: Leander
  full_name: Claes, Leander
  id: '11829'
  last_name: Claes
  orcid: 0000-0002-4393-268X
- first_name: Bernd
  full_name: Henning, Bernd
  id: '213'
  last_name: Henning
citation:
  ama: 'Spieker C, Förstner J, Hölscher J, Claes L, Henning B. Modeling and simulation
    of the behavior of piezoceramics with the discontinuous Galerkin method. In: <i>2025
    International Congress on Ultrasonics</i>. AMA Service GmbH; 2025:126–129. doi:<a
    href="https://doi.org/10.5162/ultrasonic2025/a18-a1">10.5162/ultrasonic2025/a18-a1</a>'
  apa: Spieker, C., Förstner, J., Hölscher, J., Claes, L., &#38; Henning, B. (2025).
    Modeling and simulation of the behavior of piezoceramics with the discontinuous
    Galerkin method. <i>2025 International Congress on Ultrasonics</i>, 126–129. <a
    href="https://doi.org/10.5162/ultrasonic2025/a18-a1">https://doi.org/10.5162/ultrasonic2025/a18-a1</a>
  bibtex: '@inproceedings{Spieker_Förstner_Hölscher_Claes_Henning_2025, place={Paderborn},
    title={Modeling and simulation of the behavior of piezoceramics with the discontinuous
    Galerkin method}, DOI={<a href="https://doi.org/10.5162/ultrasonic2025/a18-a1">10.5162/ultrasonic2025/a18-a1</a>},
    booktitle={2025 International Congress on Ultrasonics}, publisher={AMA Service
    GmbH}, author={Spieker, Carsten and Förstner, Jens and Hölscher, Jonas and Claes,
    Leander and Henning, Bernd}, year={2025}, pages={126–129} }'
  chicago: 'Spieker, Carsten, Jens Förstner, Jonas Hölscher, Leander Claes, and Bernd
    Henning. “Modeling and Simulation of the Behavior of Piezoceramics with the Discontinuous
    Galerkin Method.” In <i>2025 International Congress on Ultrasonics</i>, 126–129.
    Paderborn: AMA Service GmbH, 2025. <a href="https://doi.org/10.5162/ultrasonic2025/a18-a1">https://doi.org/10.5162/ultrasonic2025/a18-a1</a>.'
  ieee: 'C. Spieker, J. Förstner, J. Hölscher, L. Claes, and B. Henning, “Modeling
    and simulation of the behavior of piezoceramics with the discontinuous Galerkin
    method,” in <i>2025 International Congress on Ultrasonics</i>, 2025, pp. 126–129,
    doi: <a href="https://doi.org/10.5162/ultrasonic2025/a18-a1">10.5162/ultrasonic2025/a18-a1</a>.'
  mla: Spieker, Carsten, et al. “Modeling and Simulation of the Behavior of Piezoceramics
    with the Discontinuous Galerkin Method.” <i>2025 International Congress on Ultrasonics</i>,
    AMA Service GmbH, 2025, pp. 126–129, doi:<a href="https://doi.org/10.5162/ultrasonic2025/a18-a1">10.5162/ultrasonic2025/a18-a1</a>.
  short: 'C. Spieker, J. Förstner, J. Hölscher, L. Claes, B. Henning, in: 2025 International
    Congress on Ultrasonics, AMA Service GmbH, Paderborn, 2025, pp. 126–129.'
date_created: 2025-11-25T12:23:05Z
date_updated: 2026-06-08T17:55:26Z
department:
- _id: '49'
- _id: '61'
doi: 10.5162/ultrasonic2025/a18-a1
keyword:
- tet_topic_piezo
language:
- iso: eng
page: 126–129
place: Paderborn
project:
- _id: '245'
  name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken
    für Leistungsschallanwendungen (NEPTUN)'
publication: 2025 International Congress on Ultrasonics
publisher: AMA Service GmbH
status: public
title: Modeling and simulation of the behavior of piezoceramics with the discontinuous
  Galerkin method
type: conference
user_id: '158'
year: '2025'
...