OPTIMAL CONTROL PROBLEM DESCRIBING BY THE CAUCHY PROBLEM FOR THE FIRST ORDER LINEAR HYPERBOLIC SYSTEM WITH TWO INDEPENDENT VARIABLES

In the paper optimal control problems are considered, describing by the Cauchy problem for the first order linear hyperbolic system with two independent variables and integral quadratic functional. The existence and uniqueness theorems of the optimal control are proved. Necessary and sufficient conditions of optimality are derived. Finding of the optimal control and minimum of the functional is reduced to the solution of the non-linear system of integro- differential equations.