TY - JOUR

T1 - Measure-valued solutions for the equations of polyconvex adiabatic thermoelasticity

AU - Christoforou, Cleopatra

AU - Galanopoulou, Myrto Maria

AU - Tzavaras, Athanasios

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2019/8/30

Y1 - 2019/8/30

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/656727

UR - http://aimsciences.org//article/doi/10.3934/dcds.2019269

UR - http://www.scopus.com/inward/record.url?scp=85071259008&partnerID=8YFLogxK

U2 - 10.3934/dcds.2019269

DO - 10.3934/dcds.2019269

M3 - Article

SN - 1553-5231

VL - 39

SP - 6175

EP - 6206

JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

IS - 11

ER -