Asymptotic calculation of the heat distribution in a plane

Abstract

For the heat equation in the plane, an asymptotic approximation of the solution of the Cauchy problem for large times is constructed in the case where the initial function has a power-like asymptotics at infinity. In addition to direct application to heat conduction and diffusion processes, the study of the asymptotic behavior of the solution of the problem under consideration is of independent interest for the asymptotic analysis.