DZHUMABAEV PARAMETERIZATION METHOD FOR SOLVING AN INITIAL–BOUNDARY VALUE PROBLEMFOR HIGHER ORDER PARTIAL DIFFERENTIAL EQUATIONS

Abstract

Weconsideran application ofthe Dzhumabaev parameterization method for solving initial-boundary value problems for higher order partial differential equations with two variables. These problems are reduced to nonlocal problems for system of hyperbolic equations of second order with mixed derivatives, or to the family of boundary value problems for hybrid systems consisting of first order partial differential equations, or systems of ordinary differential equations with a parameter and functional relations. A family of multipoint boundary value problems for higher order differential equations is solved by the Dzhumabaev parameterization method. The methods and results are developed to nonlocal problems for higher order par-tial differential equations with loading and delay arguments, nonlocal problems with integral conditionsand impulse effects for higher order partial differential equations.