Abstract
In this paper we examine integrodifferential evolution inclusions of the Volterra type driven by time dependent, monotone, hemicontinuous operators. We prove two existence theorems; one for convex valued perturbations and the other for nonconvex valued ones. We also establish a topological property of the solution set of the “convex” problem. Then we prove a result on the continuous dependence of the solutions on the data of the problem (sensitivity analysis). We also consider a random version of the inclusion and prove that it admits a random solution. Then we pass to optimal control problems. First we establish the existence of optimal admissible pairs and then using the notions of epigraphical and G-convergences, we obtain a variational stability result. Finally we work in detail two parabolic distributed parameter optimal control problems, illustrating the applicability of our work.
