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

Myrto Galanopoulou; Andreas Vikelis; Konstantinos Koumatos

doi:10.1080/03605302.2022.2047725

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

Myrto Galanopoulou, Andreas Vikelis^*, Konstantinos Koumatos

^*Corresponding author for this work

University of Sussex

Research output: Contribution to journal › Article › peer-review

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 Gårding-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.

Original language	English
Pages (from-to)	1133-1175
Number of pages	43
Journal	Communications in Partial Differential Equations
Volume	47
Issue number	6
Early online date	24 Mar 2022
DOIs	https://doi.org/10.1080/03605302.2022.2047725
Publication status	Published - 3 Jun 2022

Keywords

Gårding inequalities
measure-valued solutions
quasiconvexity
Thermoelasticity
weak vs strong uniqueness

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1080/03605302.2022.2047725

Cite this

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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.",

keywords = "G{\aa}rding inequalities, measure-valued solutions, quasiconvexity, Thermoelasticity, weak vs strong uniqueness",

author = "Myrto Galanopoulou and Andreas Vikelis and Konstantinos Koumatos",

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AU - Vikelis, Andreas

AU - Koumatos, Konstantinos

N1 - Funding Information: KK and AV acknowledge the support of the Dr Perry James (Jim) Browne Research Centre on Mathematics and its Applications of the University of Sussex. The article was partially written while MG was a PhD student at King Abdullah University of Science and Technology (KAUST), Saudi Arabia. Publisher Copyright: © 2022 Taylor & Francis Group, LLC.

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N2 - 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 Gårding-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.

AB - 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 Gårding-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.

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KW - measure-valued solutions

KW - quasiconvexity

KW - Thermoelasticity

KW - weak vs strong uniqueness

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JF - Communications in Partial Differential Equations

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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