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On a homogeneous parabolic problem in an infinite angular domain
M. T. Jenaliyeva, M. I. Ramazanovb, S. A. Iskakovb a Institute of Mathematics and Mathematical Modeling, Pushkin 125, Almaty, Kazakhstan
b Buketov Karaganda State University, Universitetskaya 28, Karaganda, Kazakhstan
Abstract:
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.
Citation:
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, 7:1 (2019), 38–52
Linking options:
https://www.mathnet.ru/eng/ejmca130 https://www.mathnet.ru/eng/ejmca/v7/i1/p38
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