American Institute of Mathematical Sciences

November  2019, 39(11): 6175-6206. doi: 10.3934/dcds.2019269

Measure-valued solutions for the equations of polyconvex adiabatic thermoelasticity

 1 Department of Mathematics and Statistics, University of Cyprus, Nicosia 1678, Cyprus 2 Computer, Electrical, Mathematical Sciences & Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia

* Corresponding author: Christoforou was partially supported by the Internal grant SBLawsMechGeom #21036 from University of Cyprus

Received  August 2018 Revised  November 2018 Published  August 2019

Fund Project: This project has received funding from the European Union's Horizon 2020 programme under the Marie Sklodowska-Curie grant agreement No 642768

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.

Citation: Cleopatra Christoforou, Myrto Galanopoulou, Athanasios E. Tzavaras. Measure-valued solutions for the equations of polyconvex adiabatic thermoelasticity. Discrete & Continuous Dynamical Systems - A, 2019, 39 (11) : 6175-6206. doi: 10.3934/dcds.2019269
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