Weak-strong uniqueness for measure-valued solutions to the equations of quasiconvex adiabatic thermoelasticity

TL;DR

This paper proves a weak-strong uniqueness principle for measure-valued solutions to quasiconvex adiabatic thermoelasticity equations, using a G{ a}rding-type inequality under specific internal energy assumptions.

Contribution

It introduces a G{ a}rding-type inequality for quasiconvex functions and applies it to establish weak-strong uniqueness for measure-valued solutions in thermoelasticity.

Findings

Established a G{ a}rding-type inequality for quasiconvex functions.

Proved weak-strong uniqueness for dissipative measure-valued solutions.

Linked quasiconvexity and symmetrisability in thermoelastic systems.

Abstract

This article studies the equations of adiabatic thermoelasticity endowed with an internal energy satisfying an appropriate quasiconvexity assumption which is associated to the symmetrisability condition for the system. A G{\aa}rding-type inequality for these quasiconvex functions is proved and used to establish a weak-strong uniqueness result for a class of dissipative measure-valued solutions.