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

Cleopatra Christoforou, Athanasios Tzavaras

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)1-52
Number of pages52
JournalArchive for Rational Mechanics and Analysis
Volume229
Issue number1
DOIs
StatePublished - Dec 21 2017

Fingerprint

Dive into the research topics of 'Relative entropy for hyperbolic-parabolic systems and application to the constitutive theory of thermoviscoelasticity'. Together they form a unique fingerprint.

Cite this