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, Mathematical Sciences & Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia.
Publisher:
arXiv
Issue Date:
5-Nov-2017
ARXIV:
arXiv:1711.01582
Type:
Preprint
Additional Links:
http://arxiv.org/abs/1711.01582v1; http://arxiv.org/pdf/1711.01582v1
Appears in Collections:
Other/General Submission; Temporary Processing

Full metadata record

DC FieldValue Language
dc.contributor.authorChristoforou, Cleopatraen
dc.contributor.authorGalanopoulou, Myrto Mariaen
dc.contributor.authorTzavaras, Athanasiosen
dc.date.accessioned2017-12-28T07:32:11Z-
dc.date.available2017-12-28T07:32:11Z-
dc.date.issued2017-11-05en
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.publisherarXiven
dc.relation.urlhttp://arxiv.org/abs/1711.01582v1en
dc.relation.urlhttp://arxiv.org/pdf/1711.01582v1en
dc.rightsArchived with thanks to arXiven
dc.titleA symmetrizable extension of polyconvex thermoelasticity and applications to zero-viscosity limits and weak-strong uniquenessen
dc.typePreprinten
dc.contributor.departmentComputer, Electrical, Mathematical Sciences & Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia.en
dc.eprint.versionPre-printen
dc.contributor.institutionDepartment of Mathematics and Statistics, University of Cyprus, Nicosia 1678, Cyprus.en
dc.identifier.arxividarXiv:1711.01582en
kaust.authorGalanopoulou, Myrto Mariaen
kaust.authorTzavaras, Athanasiosen
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