ABSTRACT
In this chapter we examine nonlinear parabolic optimal control problems involving multivalued terms. First we consider a Lagrange optimal control problem with the differential operator being in divergence form and nonmonotone. Then we turn our attention to parametric problems with a nonlinear, multivalued, maximal monotone differential operator. In this case the relevant problem is a minimax problem in which we minimize the maximum cost over all parameters. We prove the existence of an optimal control using the notion of G-convergence of operators.
Keywords and Phrases: Evolution triple, compact embedding, upper and lower semicontinuous multifunctions, measurable multifunctions, measurable selection, monotone operator, pseudomonotone operator, L-generalized pseudomonotone operator, G-convergence, τ-topology, optimal control, minimax problem
1990 AMS Subject Classification: 49J35, 49J27
