ABSTRACT

Introduction This note is, in a sense, a continuation of the papers of Denkowski [5] and Denkowski and Migo´rski [7] concerning the sensitivity of optimal solutions to control problems for systems governed by the stationary (elliptic) and the first order evolution (parabolic) hemivariational inequalities (HVIs). Here our main results provide sufficient conditions for the variational convergence of optimal solutions of perturbed control

problems for systems governed by second order evolution (hyperbolic) HVIs. We consider two special classes of such HVIs: with multivalued and time independent, and single-valued and time dependent damping.