A Multi-Point Initial Problem for a Non-Classical System of a Partial Differential Equations

Abstract

Multi-point initial boundary value problem for fourth order system of partial differential equations is considered. By new unknown function the problem is reduced to an equivalent nonlocal problem for system of hyperbolic equations of second order with dynamical condition. By the method of introduction functional parameters are constructed the algorithms for finding of solution to nonlocal problem for system of hyperbolic equations of second order with dynamical condition. Conditions of existence unique classical solution to nonlocal problem for system of hyperbolic equations of second order with dynamical condition are obtained in the terms of initial data. Criteria of unique solvability to multi-point initial boundary value problem for fourth order system of partial differential equations is established.