Optimizing Control for a Piezo-Viscoelastic Contact Challenge Involving Normal Compliance and Coulomb’s Friction

The objective of this paper is to investigate an optimal control problem related to a frictional contact problem involving a piezo-viscoelastic body and an electrically conductive foundation. The contact procedure is characterized by a compliance normal condition combined with a version of Coulomb’s friction law. A variational formulation of the model is developed, resulting in a coupled system for the displacement files and electric potentials. We establish the existence and uniqueness results for a weak solution under the assumption of a smallness condition. Finally, we establish the existence of optimal solutions for two classes of optimal control problems and inverse problems which are described by the piezo-viscoelastic contact problem under consideration