On the existence of an optimal solution of the Mayer problem governed by 2D continuous counterpart of the Fornasini-Marchesini model

Abstract

In the paper the optimization problem described by some nonlinear hyperbolic equation being continuous counterpart of the Fornasini-Marchesini model is considered. A theorem on the existence of at least one solution to this hyperbolic PDE is proved and some properties of the set of all solutions are established. The existence of a solution to an optimization problem under appropriate assumptions is themain result of this paper. Some application of the obtained results to the process of gas filtration is also presented.