| Abstract: |
| We consider a class of optimal control problems for abstract hemivariational inequalities with a history-dependent operator. Based on the solvability of associated nonlinear evolution inclusions with history-dependent operators considered on Sobolev spaces, we review recent results on the existence and uniquenes of a weak solution to hemivariational inequalities. Then we consider the Bolza distributed parameter control problem. We deliver results on the continuous dependence of the solution to hemivariational inequality on the control parameter. By applying the direct method of calculus of variations, we provide conditions that gwarantee the existence of optimal solutions to control problems. Finally, we provide a mechanical model to which the theory applies. |
|