Averaging in the optimal control problem for the reaction-diffusion equation with multivalued interaction function

In this paper consider the optimal control problem on infinite time interval with quadratic cost functional. State of this problem is defined by the evolutionary inclusion of reaction-diffusion type. We prove the solvability of such a problem. In the case of rapidly oscillating coefficients in coefficients of differential operator and multivalued interaction function we prove the convergence of $\varepsilon $-dependent optimal process to optimal process of the corresponding averaged problem.