### AN OPTIMAL CONTROL TO SOLUTIONS OF THE SHOWALTER-SIDOROV PROBLEM FOR THE HOFF MODEL ON THE GEOMETRICAL GRAPH

#### Abstract

A lot of initial-boundary value problems for the equations and the systems of equations which are not resolved with respect to time derivative are considered in the framework of abstract Sobolev type equations that make up the vast field of non-classical equations of mathematical physics. We are interested in the optimal control problem to solutions of the Showalter -Sidorov problem for the semilinear Sobolev type equation. In this research we demonstrate the appliance of the abstract scheme to the solution of optimal control problem for the Hoff equations on a graph. The physical sense of the optimal control problem lies in the fact that the construction of I-beams should assume the desired shape with minimal costs. This scheme is based on the Galerkin method, allowing carrying out computational experiments. The sufficient conditions for the existence of optimal control to solutions of the Showalter - Sidorov problem for the Hoff equation on the geometrical graph are found.

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