On a Problem of Optimal Control for a Nonlinear Pseudohyperbolic Equation

In this article, it is considered some questions of approximation solving of an optimal control problem for nonlinear partial pseudohyperbolic differential equations of the fifth order with initial-boundary value conditions and general view of the optimality criterion. Using the method of separation of variables in the form of a Fourier series reduces the generalized solution of the initial-boundary value problem to a countable system of nonlinear integral equations. By the aid of the methods of successive approximations and integral inequalities it is studied the one-value solvability of a finite system of nonlinear integral equations for the fixed values of the control, which are bounded by the given positive constant. It is estimated the permissible error with respect to a state of a “shorter” generalized solution of the initial-boundary value problem. Further, it is proved that the control sequence is a minimizing sequence for the considered problem.