A symmetrizable extension of polyconvex thermoelasticity and applications to zero-viscosity limits and weak-strong uniqueness
Type
ArticleKAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2018-04-20Preprint Posting Date
2017-11-05Permanent link to this record
http://hdl.handle.net/10754/626459
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We embed the equations of polyconvex thermoviscoelasticity into an augmented, symmetrizable, hyperbolic system and derive a relative entropy identity in the extended variables. Following the relative entropy formulation, we prove the convergence from thermoviscoelasticity with Newtonian viscosity and Fourier heat conduction to smooth solutions of the system of adiabatic thermoelasticity as both parameters tend to zero. Also, convergence from thermoviscoelasticity to smooth solutions of thermoelasticity in the zero-viscosity limit. Finally, we establish a weak-strong uniqueness result for the equations of adiabatic thermoelasticity in the class of entropy weak solutions.Citation
Christoforou, C., Galanopoulou, M., & Tzavaras, A. E. (2018). A symmetrizable extension of polyconvex thermoelasticity and applications to zero-viscosity limits and weak-strong uniqueness. Communications in Partial Differential Equations, 43(7), 1019–1050. doi:10.1080/03605302.2018.1456551Publisher
Informa UK LimitedarXiv
1711.01582Additional Links
http://arxiv.org/abs/1711.01582v2http://arxiv.org/pdf/1711.01582v2
ae974a485f413a2113503eed53cd6c53
10.1080/03605302.2018.1456551