The differential-symbol method of constructing the quasipolynomial solutions of two-point in time problem for nonhomogeneous partial differential equation

Abstract

The existence of the solution of nonhomogeneous partial differential equations (PDE) of second order in timeand finite or infinite order in spatial variable with quasipolynomial right-hand side is proved. This solution satisfies thehomogeneous two-point in time conditions. The differential-symbol method for constructing the solution of the problemis proposed. The examples of applying this method for solving some two-point problems for PDE are suggested.