Operational calculus approach to explicit solving of initial and boundary value problems

Abstract

Short review of an approach to explicit solving of initial and boundary value problems (BVPs) for some partial differential equations (PDEs) is presented. A combination of two classical methods—the Fourier method and the Duhamel principle—are used in the frames of a two-dimensional operational calculus suggested in [1]. It gives explicit solutions of some local and non-local BVPs for the classical equations of Mathematical Physics in rectangular domains.