On solving intial-boundary value problem for system of equations in partial derivatives of the third order

We consider the initial-boundary value problem for the system of partial differential equations of third order. We investigate the questions of an existence unique classical solution to the considering problem and approaches of its construction. By the introduction of new unknown function the initial-boundary value problem for the system of partial differential equations of third order is reduced to an equivalent nonlocal problem with integral condition for the system of integro-differential equations of hyperbolic type and functional relation. Conditions of a unique solvability to the nonlocal problem with integral condition for the system of integro-differential equations hyperbolic type and functional relation are obtained based on the method of introduction functional parameters. Algorithms for finding a solution of the equivalent problem are proposed and their convergence are proved. Conditions of the existence unique classical solution to the initial-boundary value problem for the system of partial differential equations of third order are established in the terms of initial data.