Geodesic
On a homogeneous parabolic problem in an infinite angular domain
Eurasian journal of mathematical and computer applications, Tome 7 (2019) no. 1, pp. 38-52.

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In this paper we study a homogeneous boundary value problem for the heat equation in a noncylindrical domain with the special boundary conditions. The problem under consideration is useful for solving the single-phase Stefan problem. It has been shown that this homogeneous problem has a nontrivial solution up to constant factor in the weight class of essentially bounded functions. A class of functions in which this problem has only a trivial solution is found. Thus, a class of functions in which the corresponding inhomogeneous problem is uniquely solvable is defined.
Keywords: Stefan’s problem, heat equation, noncylindrical domain. 
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     title = {On a homogeneous parabolic problem in an infinite angular domain},
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M. T. Jenaliyev; M. I. Ramazanov; S. A. Iskakov. On a homogeneous parabolic problem in an infinite angular domain. Eurasian journal of mathematical and computer applications, Tome 7 (2019) no. 1, pp. 38-52. http://geodesic.mathdoc.fr/item/EJMCA_2019_7_1_a2/