On a determination of the boundary function in the initial-boundary value problem for the second order hyperbolic equation

Abstract

In the paper the problem of determination of the boundary function is studied in the initial boundary value problem described by the second order hyperbolic equation. With the help of the additional condition, the functional is constructed, and the problem under consideration is reduced to the optimal control problem. The differential of the function is calculated, a necessary and sufficient condition for optimality is proved.