Optimal control of doubly nonlinear evolution equations governed by subdifferentials without uniqueness of solutions

Abstract

In this paper we study an optimal control problem for a doubly nonlinear evolution equation governed by time-dependent subdifferentials. We prove the existence of solutions to our equation. Also, we consider an optimal control problem without uniqueness of solutions to the state system. Then, we prove the existence of an optimal control which minimizes the nonlinear cost functional. Moreover, we apply our general result to some model problem.