Relative entropy for hyperbolic-parabolic systems and application to the constitutive theory of thermoviscoelasticity

Handle URI:
http://hdl.handle.net/10754/603957
Title:
Relative entropy for hyperbolic-parabolic systems and application to the constitutive theory of thermoviscoelasticity
Authors:
Christoforou, Cleopatra; Tzavaras, Athanasios ( 0000-0002-1896-2270 )
Abstract:
We extend the relative entropy identity to the class of hyperbolic-parabolic systems whose hyperbolic part is symmetrizable. The resulting identity is useful to provide measure valued weak versus strong uniqueness theorems for the hyperbolic problem. Also, it yields a convergence result in the zero-viscosity limit to smooth solutions in an Lp framework. The relative entropy identity is also developed for the system of gas dynamics for viscous and heat conducting gases, and for the system of thermoviscoelasticity with viscosity and heat-conduction. Existing differences between the example and the general hyperbolic theory are underlined.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Issue Date:
27-Mar-2016
ARXIV:
1603.08176
Type:
Article
Sponsors:
Research partially supported by the European Commission ITN project ”Modeling and computation of shocks and interfaces”. AET acknowledges the support of the King Abdullah University of Science and Technology (KAUST).
Additional Links:
http://arxiv.org/abs/1603.08176
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorChristoforou, Cleopatraen
dc.contributor.authorTzavaras, Athanasiosen
dc.date.accessioned2016-03-30T07:33:38Zen
dc.date.available2016-03-30T07:33:38Zen
dc.date.issued2016-03-27en
dc.identifier.urihttp://hdl.handle.net/10754/603957en
dc.description.abstractWe extend the relative entropy identity to the class of hyperbolic-parabolic systems whose hyperbolic part is symmetrizable. The resulting identity is useful to provide measure valued weak versus strong uniqueness theorems for the hyperbolic problem. Also, it yields a convergence result in the zero-viscosity limit to smooth solutions in an Lp framework. The relative entropy identity is also developed for the system of gas dynamics for viscous and heat conducting gases, and for the system of thermoviscoelasticity with viscosity and heat-conduction. Existing differences between the example and the general hyperbolic theory are underlined.en
dc.description.sponsorshipResearch partially supported by the European Commission ITN project ”Modeling and computation of shocks and interfaces”. AET acknowledges the support of the King Abdullah University of Science and Technology (KAUST).en
dc.language.isoenen
dc.relation.urlhttp://arxiv.org/abs/1603.08176en
dc.titleRelative entropy for hyperbolic-parabolic systems and application to the constitutive theory of thermoviscoelasticityen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.eprint.versionPre-printen
dc.contributor.institutionDepartment of Mathematics and Statistics, University of Cyprus, Nicosia 1678, Cyprusen
dc.contributor.institutionInstitute of Applied and Computational Mathematics, FORTH, Heraklion, Greeceen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
dc.identifier.arxivid1603.08176en
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