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Continuous dependence results for subdifferential inclusions. (English) Zbl 0777.34042

The paper deals with the parametrized class of nonlinear evolution inclusions of subdifferential type (1) \(-\dot x(t)\in\partial\varphi(x(t),\lambda)+F(t,x(t),\lambda)\) a.e., \(x(0)=x_ 0(\lambda)\). The author studies continuity properties of the multifunction \(\lambda\to S(\lambda)\), where \(S(\lambda)\) is the set of strong solutions of (1). He finds conditions under which the solution set depends continuously on \(L\) for both the Victoris and Hausdorff topologies. Then, using these interesting results, he studies the variational stability of a class of nonlinear distributed parameter optimal control problems. He also shows how these results incorporate the stability analysis of differential variational inequalities.

MSC:

34G20 Nonlinear differential equations in abstract spaces
49J20 Existence theories for optimal control problems involving partial differential equations
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