Optimal control of states for a nonstationary model in the relatively radial case

In this paper we prove the existence of a unique optimal and hard control over solutions of Showalter–Sidorov problem for the nonstationary model, which is described by Sobolev type equations. In this case, one of the operators in the equation is multiplied by a scalar function of the time-variable, besides stationary equation has a strong continuous degenerate resolving semigroup of operators.