# Article

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Keywords:
subdifferential; compact type; Vietoris topology; Hausdorff metric; parabolic optimal control problem
Summary:
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.
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