Integral transforms and boundary value problems

Abstract

This article is devoted to determine the solution of the none stationary heat conduction equation for unlimited space and to investigate the two-dimensional Helmholtz equation. The solutions of the considered boundary value problems are obtained with the use of the mixed Fourier transform and of the double Fourier transform. From these line items in work it is illustrated how the integral transforms method can be used to obtain the solution of boundary value problems for partial differential equations of different kinds. In addition, the Green’s function is built for the two-dimensional Poisson equation in this article.