The present monograph concerns the study of an evolution inclusion of subdifferential type:
The function is assumed to be convex, and the symbol “” is understood as the subdifferential operator in the sense of convex analysis. Here is a nonmonotone set-valued perturbation with a time varying domain which satisfies a certain growth condition, and is a separable Hilbert space. The authors discuss several issues related to the above evolution system: existence of solutions, relaxation, dependence of the solution set on external parameters, path-connectedness of the solution set. In a second part, the authors discuss an abstract optimal control problem which consists in minimizing the cost functional
among all trajectories satisfying the evolution inclusion (E), and all measurable controls satisfying the feedback inclusion
Special attention is paid to existence results, relaxability, and well-posedness.