ASYMPTOTIC-BEHAVIOR OF OPTIMAL-SOLUTIONS TO CONTROL-PROBLEMS FOR SYSTEMS DESCRIBED BY DIFFERENTIAL-INCLUSIONS CORRESPONDING TO PARTIAL-DIFFERENTIAL EQUATIONS

In the paper, we consider differential inclusions related to PDEs of p arabolic type and some control problems with integral cost functionals associated to them. Given a sequence of such problems, we investigate first the asymptotic behavior of solution sets (mild solutions or mor e precisely selection-trajectory pairs) for differential inclusions, a nd we get some semicontinuity or continuity results (Kuratowski conver gence of solution sets). Then, we prove the GAMMA-convergence of cost functionals, related to the above Kuratowski convergence of solution s ets. Finally, applying the Buttazzo-Dal Maso abstract scheme, based on the sequential GAMMA-convergence, we obtain results concerning the as ymptotic behavior (hence, also stability results) for optimal solution s to control problems as well as the convergence of minimal values.