A symmetrizable extension of polyconvex thermoelasticity and applications to zero-viscosity limits and weak-strong uniqueness

Handle URI:
http://hdl.handle.net/10754/626459
Title:
A symmetrizable extension of polyconvex thermoelasticity and applications to zero-viscosity limits and weak-strong uniqueness
Authors:
Christoforou, Cleopatra; Galanopoulou, Myrto Maria; Tzavaras, Athanasios ( 0000-0002-1896-2270 )
Abstract:
We embed the equations of polyconvex thermoviscoelasticity into an augmented, symmetrizable, hyperbolic system and derive a relative entropy identity in the extended variables. Following the relative entropy formulation, we prove the convergence from thermoviscoelasticity with Newtonian viscosity and Fourier heat conduction to smooth solutions of the system of adiabatic thermoelasticity as both parameters tend to zero. Also, convergence from thermoviscoelasticity to smooth solutions of thermoelasticity in the zero-viscosity limit. Finally, we establish a weak-strong uniqueness result for the equations of adiabatic thermoelasticity in the class of entropy weak solutions.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program; Computer, Electrical, Mathematical Sciences & Engineering Division
Publisher:
Taylor & Francis
Journal:
Communications in Partial Differential Equations
Issue Date:
21-Mar-2018
DOI:
10.1080/03605302.2018.1456551
ARXIV:
arXiv:1711.01582
Type:
Article
Additional Links:
http://arxiv.org/abs/1711.01582v2; http://arxiv.org/pdf/1711.01582v2
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorChristoforou, Cleopatraen
dc.contributor.authorGalanopoulou, Myrto Mariaen
dc.contributor.authorTzavaras, Athanasiosen
dc.date.accessioned2018-03-22T13:30:01Z-
dc.date.available2017-12-28T07:32:11Z-
dc.date.available2018-03-22T13:30:01Z-
dc.date.issued2018-03-21-
dc.identifier.doi10.1080/03605302.2018.1456551-
dc.identifier.urihttp://hdl.handle.net/10754/626459-
dc.description.abstractWe embed the equations of polyconvex thermoviscoelasticity into an augmented, symmetrizable, hyperbolic system and derive a relative entropy identity in the extended variables. Following the relative entropy formulation, we prove the convergence from thermoviscoelasticity with Newtonian viscosity and Fourier heat conduction to smooth solutions of the system of adiabatic thermoelasticity as both parameters tend to zero. Also, convergence from thermoviscoelasticity to smooth solutions of thermoelasticity in the zero-viscosity limit. Finally, we establish a weak-strong uniqueness result for the equations of adiabatic thermoelasticity in the class of entropy weak solutions.en
dc.language.isoenen
dc.publisherTaylor & Francisen
dc.relation.urlhttp://arxiv.org/abs/1711.01582v2en
dc.relation.urlhttp://arxiv.org/pdf/1711.01582v2en
dc.rightsArchived with thanks to Communications in Partial Differential Equationsen
dc.titleA symmetrizable extension of polyconvex thermoelasticity and applications to zero-viscosity limits and weak-strong uniquenessen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentComputer, Electrical, Mathematical Sciences & Engineering Divisionen
dc.identifier.journalCommunications in Partial Differential Equationsen
dc.eprint.versionPost-printen
dc.contributor.institutionDepartment of Mathematics and Statistics, University of Cyprus, Nicosia 1678, Cyprus.en
dc.identifier.arxividarXiv:1711.01582-
kaust.authorGalanopoulou, Myrto Mariaen
kaust.authorTzavaras, Athanasiosen

Version History

VersionItem Editor Date Summary
2 10754/626459grenzdm2018-03-22 13:27:18.568Revised version submitted by Myrto Maria Galanopoulou.
1 10754/626459.1grenzdm2017-12-28 07:32:11.0
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