In this paper we examine the dependence on a parameter of the solution set of a class of nonlinear evolution inclusions driven by subdifferential operators. We prove that under mild hypotheses on the data, the solution set depends continuously on the parameter for both the Victoria and Rausdorif topologies. Then we use these results to study the variational stability of the class of semnilinear parabolic optimal control problems and we also indicate how our work incorporates the stability analysis of differential variational inequalities.
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Nikolaos S. Papageorgiou, Continuous Dependence Results for Subdifferential Inclusions. Z. Anal. Anwend. 12 (1993), no. 1, pp. 137–152DOI 10.4171/ZAA/575