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.

中文翻译：

---

多凸热弹性等熵过程的离散变分方案

我们提出了一个变分方案，用于构造具有多凸内能的绝热热弹性方程的等熵过程。该方案取决于将绝热多凸热弹性方程式嵌入到对称双曲系统中。我们建立了与最小化定理相关联的最小化器的存在，并构建了耗散总能量的度量值解决方案。我们证明了当极限解是光滑的时该方案收敛。