Measure-valued solutions for the equations of polyconvex adiabatic thermoelasticity

Cleopatra Christoforou, Myrto Maria Galanopoulou, Athanasios Tzavaras

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

For the system of polyconvex adiabatic thermoelasticity, we define a notion of dissipative measure-valued solution, which can be considered as the limit of a viscosity approximation. We embed the system into a symmetrizable hyperbolic one in order to derive the relative entropy. Exploiting the weak-stability properties of the transport and stretching identities, we base our analysis in the original variables, instead of the symmetric ones (in which the entropy is convex) and we prove measure-valued weak versus strong uniqueness using the averaged relative entropy inequality.
Original languageEnglish (US)
Pages (from-to)6175-6206
Number of pages32
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume39
Issue number11
DOIs
StatePublished - Aug 30 2019

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