Geodesic
Asymptotics of a solution to the heat equation with a singularity at the boundary
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 1, pp. 268-272
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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. 
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I. V. Pershin. Asymptotics of a solution to the heat equation with a singularity at the boundary. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 1, pp. 268-272. http://geodesic.mathdoc.fr/item/TIMM_2012_18_1_a20/

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