This article is cited in 1 paper

Asymptotics of a solution to the heat equation with a singularity at the boundary

I. V. Pershin

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: The third boundary value problem for a second-order parabolic equation in a half-space with singularity is considered. The singularity consists in the presence of a moving band heat source with delta-like source intensity function at the boundary of the domain. An exact analytic solution of the problem is found, and the behavior of this solution in a neighborhood of the singularity is investigated.

Keywords: boundary value problems for partial differential equations, asymptotics of a solution.

UDC: 517.977

Received: 02.09.2011

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