Optimal Control Problems for Evolutionary Variational Inequalities with Volterra-Type Operators

In this paper, we consider an optimal control problem for a class of evolution inclusions with Volterra -type operators. The existence and uniqueness results for the initial value problem for such inclusions were obtained in our previous work. Here 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, processes of electro-wetting on dielectrics, and others.