ON THE INITIAL-BOUNDARY VALUE PROBLEM FOR SYSTEM OF THE PARTIAL DIFFERENTIAL EQUATIONS OF FOURTH ORDER

A initial-boundary value problem for system of the partial differential equations of fourth order is considered. We study the existence of classical solutions to the initial-boundary value problem for system of the partial differential equations of fourth order and offer the methods for finding its approximate solutions. Sufficient conditions for the existence and uniqueness of a classical solution to the initial-boundary value problem for system of the partial differential equations of fourth order are set. By introducing of a new unknown functions, we reduce the considered problem to an equivalent problem consisting of a nonlocal problem for the system of hyperbolic equations of second order with functional parameters and the integral relations. We offer the algorithm for finding an approximate solution to the investigated problem and prove its convergence. Sufficient conditions for the existence of unique solution to the equivalent problem with parameters are established. Conditions of unique solvability to the initial-boundary value problem for system of the partial differential equations of fourth order are obtained in the terms of initial data. Separately, the result is given for the initial-periodic in time boundary value problem.