Measure-valued solutions for the equations of polyconvex adiabatic thermoelasticity
Name:
thermo-poly-mv_SUBMIT_arxiv.pdf
Size:
481.0Kb
Format:
PDF
Description:
Accepted manuscript
Type
ArticleKAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2019-08-30Online Publication Date
2019-08-30Print Publication Date
2019Embargo End Date
2020-01-01Permanent link to this record
http://hdl.handle.net/10754/656727
Metadata
Show full item recordAbstract
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
Christoforou, C., Galanopoulou, M., & E. Tzavaras, A. (2019). Measure-valued solutions for the equations of polyconvex adiabatic thermoelasticity. Discrete & Continuous Dynamical Systems - A, 39(11), 6175–6206. doi:10.3934/dcds.2019269Additional Links
http://aimsciences.org//article/doi/10.3934/dcds.2019269ae974a485f413a2113503eed53cd6c53
10.3934/dcds.2019269