On a boundary value problem for the nonhomogeneous heat equation in an angular domain

Abstract

Due to the fact that the results find theoretical and practical applications, great attention is paid to the study of boundary value problems for parabolic equations. Also the relevance of studying such problems is justified by their physical application in the modeling of such processes as the propagation of heat in homogeneous and nonhomogeneous media, the interaction of filtration and channel flows, and other. Therefore, at the present stage of its development, the theory of partial differential equations is one of the important branches of mathematics and is actively developed by various mathematical schools. However, a number of significant problems in the theory of partial differential equations remain, as before, unresolved. In the paper we study a boundary value problem for the nonhomogeneous heat equation in an angular domain. Note that the problem does not have the initial condition. It is caused by the form of the domain. We obtain a boundary condition for the nonhomogeneous heat equation considered in the angular domain. It is proven that the heat potential is a unique classical solution to this problem.

Keywords

• heat equation
• green’s function
• classical solution