The numerical solution to the optimal control problem for the nonstationary Dzektser model

Of concern is a numerical solution to the optimal control problem for the operator-differential equation, unsolved with respect to the derivative by time, with Showalter – Sidorov condition. Such equations are called Sobolev type equations. Sobolev type equations now constitute a vast area of nonclassical equations of mathematical physics. So in this article we construct a numerical solution to the optimal control problem for the nonstationary Dzektser model with Showalter – Sidorov condition. Besides the introduction and bibliography article comprises three parts. The first part provides essential information regarding the theory of relatively $p$-sectorial operators. Also in this part the existence of solutions for optimal control problem with Showalter – Sidorov condition. The optimal control problem over solutions of Dzektser model is described in the second part. The third one contains the results of the numerical solution of optimal control problem for Dzektser model considered on a rectangle.