Stability and optimal control for differential constrained variational-hemivariational inequalities

In this paper we analyze a differential variational-hemivariational inequality which consists of an evolution equation of first order and a time-dependent constrained variational-hemivariational inequality. First, we present a new stability result for the solution set with respect to a control parameter. Then, we derive an existence result for a general optimal control problem for the differential variational-hemivariational inequality. We provide an application of the results to a weak formulation of a quasistatic frictional elastic contact problem. A stability result of a set of weak solutions with respect to the densities of volume forces, tractions and heat sources, and the initial conditions for the temperature is examined. Finally, an existence of solutions for an optimal control problem for the contact model is discussed.