Abstract:In this paper we study evolution inclusions generated by time dependent convex subdifferentials, with the orientor field $F$ depending on a parameter. Under reasonable hypotheses on the data, we show that the solution set $S(\lambda )$ is both Vietoris and Hausdorff metric continuous in $\lambda \in \Lambda $. Using these results, we study the variational stability of a class of nonlinear parabolic optimal control problems.
Keywords: subdifferential, compact type, Vietoris topology, Hausdorff metric, parabolic optimal control problem
AMS Subject Classification: 34G20, 49A20