Optimal Control Problems for Evolutionary Variational Inequalities with Volterra type Operators

In this paper, we consider the optimal control problem for a class of evolution inclusions with Volterra type operators, which can be history-dependent. We establish the existence of a solution to the stated optimal control problem under some hypothesis on data-in. The motivation for this work comes from the optimal control problems for variational inequalities arising in the study of injection molding processes, contact mechanics, principles of electro-wetting on dielectric, and others.