A discrete variational scheme for isentropic processes in polyconvex thermoelasticity

We propose a variational scheme for the construction of isentropic processes of the equations of adiabatic thermoelasticity with polyconvex internal energy. The scheme hinges on the embedding of the equations of adiabatic polyconvex thermoelasticity into a symmetrizable hyperbolic system. We establi...

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Bibliographic Details
Published in:Calculus of variations and partial differential equations 2020-08, Vol.59 (4), Article 122
Main Authors: Christoforou, Cleopatra, Galanopoulou, Myrto, Tzavaras, Athanasios E.
Format: Article
Language:English
Subjects:
Adiabatic flow
Analysis
Calculus of Variations and Optimal Control
Optimization
Control
Energy conservation
Existence theorems
Hyperbolic systems
Internal energy
Isentropic processes
Mathematical analysis
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Systems Theory
Theoretical
Thermoelasticity
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Summary:We propose a variational scheme for the construction of isentropic processes of the equations of adiabatic thermoelasticity with polyconvex internal energy. The scheme hinges on the embedding of the equations of adiabatic polyconvex thermoelasticity into a symmetrizable hyperbolic system. We establish existence of minimizers for an associated minimization theorem and construct measure-valued solutions that dissipate the total energy. We prove that the scheme converges when the limiting solution is smooth.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-020-01766-w