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A discrete variational scheme for isentropic processes in polyconvex thermoelasticity

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Abstract

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.

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Acknowledgements

The authors thank the anonymous referee for very helpful comments that helped considerably in improving this work.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Cyprus, 1678, Nicosia, Cyprus

    Cleopatra Christoforou

  2. Computer, Electrical, Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia

    Myrto Galanopoulou & Athanasios E. Tzavaras

Authors
  1. Cleopatra Christoforou
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  2. Myrto Galanopoulou
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  3. Athanasios E. Tzavaras
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Correspondence to Myrto Galanopoulou.

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Communicated by J.Ball.

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Christoforou, C., Galanopoulou, M. & Tzavaras, A.E. A discrete variational scheme for isentropic processes in polyconvex thermoelasticity. Calc. Var. 59, 122 (2020). https://doi.org/10.1007/s00526-020-01766-w

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