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

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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 "-dependent optimal process to optimal process of the corresponding averaged problem.