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

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

6 Citations (Scopus)

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

Access to Document

10.1080/03605302.2022.2047725

Cite this

@article{7b8a914aaae34affbb4c1de34d769132,

title = "Weak-strong uniqueness for measure-valued solutions to the equations of quasiconvex adiabatic thermoelasticity",

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",

note = "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: {\textcopyright} 2022 Taylor \& Francis Group, LLC.",

year = "2022",

month = jun,

day = "3",

doi = "10.1080/03605302.2022.2047725",

language = "English",

volume = "47",

pages = "1133--1175",

journal = "Communications in Partial Differential Equations",

issn = "0360-5302",

publisher = "Taylor \& Francis",

number = "6",

}

TY - JOUR

T1 - Weak-strong uniqueness for measure-valued solutions to the equations of quasiconvex adiabatic thermoelasticity

AU - Galanopoulou, Myrto

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.

PY - 2022/6/3

Y1 - 2022/6/3

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.

KW - Gårding inequalities

KW - measure-valued solutions

KW - quasiconvexity

KW - Thermoelasticity

KW - weak vs strong uniqueness

UR - https://www.scopus.com/pages/publications/85127115100

U2 - 10.1080/03605302.2022.2047725

DO - 10.1080/03605302.2022.2047725

M3 - Article

AN - SCOPUS:85127115100

SN - 0360-5302

VL - 47

SP - 1133

EP - 1175

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

IS - 6

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this