This paper focuses on optimal control of a coupled system modeling a dynamic frictional thermo-electroviscoelastic contact problem between a piezoelectric body and an electrically and thermally conductive foundation. The material’s behavior is described by a linear thermo-viscoelectroelastic constitutive law and the contact is modeled with a compliance normal condition coupled with Coulomb’s friction law, an electric condition in the Tresca’s form and thermal condition taking into account both heat transfer and frictional heating process. The weak formulation of the problem consists of a system of two variational inequalities and nonlinear variational equations. We provide existence and uniqueness results of a weak solution to the model and, under some additional assumptions, the continuous dependence of a solution on the problem’s data. Finally, for a class of optimal control problems and inverse problems, we prove the existence of optimal solutions.

本文关注于耦合系统的最优控制，该耦合系统建模了压电体与导电和导热基础之间的动态摩擦热-电-粘弹性接触问题。材料的行为由线性热-粘弹弹性本构关系描述，并且触点以顺应性正常条件与库仑摩擦定律，特雷斯卡形式的电条件和热条件（同时考虑传热和摩擦加热过程）进行建模。问题的弱公式由两个变分不等式和非线性变分方程组成。我们提供了该模型的弱解的存在性和唯一性结果，并在某些其他假设下提供了对问题数据的连续依赖关系。最后，