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Eurasian Mathematical Journal, 2016, Volume 7, Number 2, Pages 100–105
(Mi emj227)
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This article is cited in 2 scientific papers (total in 2 papers)
Short communications
Construction of Green’s function of the Neumann problem in a ball
M. A. Sadybekova, B. T. Torebeka, B. Kh. Turmetovb a Institute of Mathematics and Mathematical Modeling, 125 Pushkin St., 050010 Almaty, Kazakhstan
b A. Yasawi International Kazakh-Turkish University, 29 Sattarhanov St.,
161200 Turkestan, Kazahstan
Abstract:
Representation of the Green’s function of the classical Neumann problem for the Poisson equation in the unit ball of arbitrary dimension is given. In constructing this function we use the representation of the fundamental solution of the Laplace equation in the form of a series. It is shown that Green’s function can be represented in terms of elementary functions and its explicit form can be written out. An explicit form of the Neumann kernel was constructed for $n = 4$ and $n = 5$.
Keywords and phrases:
Green’s function, Neumann problem, Poisson equation, Laplace operator, Neumann kernel.
Received: 07.07.2015
Citation:
M. A. Sadybekov, B. T. Torebek, B. Kh. Turmetov, “Construction of Green’s function of the Neumann problem in a ball”, Eurasian Math. J., 7:2 (2016), 100–105
Linking options:
https://www.mathnet.ru/eng/emj227 https://www.mathnet.ru/eng/emj/v7/i2/p100
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