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 -