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Journal of Computational and Engineering Mathematics, 2022, Volume 9, Issue 3, Pages 30–38
DOI: https://doi.org/10.14529/jcem220303
(Mi jcem220)
 

Computational Mathematics

The Poisson equation with Wentzell boundary conditions in the square

N. S. Goncharov

South Ural State University, Chelyabinsk, Russian Federation
Abstract: The Wentzell boundary value problems with condition for second-order linear elliptic equations were studied by various methods. Over time, condition was understood as a description of a process occurring at the boundary of the domain and influenced by processes within the domain. Since in the mathematical literature the Wentzell boundary conditions has been considered from the two points of view (in classical and neoclassical cases), the purpose of this work is to show the solvability of the Wentzel problem for the Poisson equation in the square in neoclassical one, when we divide the desired function into two components.
Keywords: Laplace operator, Wentzell boundary condition, Fourier series.
Received: 31.08.2022
Document Type: Article
UDC: 519.63
MSC: 35G15, 65N30
Language: English
Citation: N. S. Goncharov, “The Poisson equation with Wentzell boundary conditions in the square”, J. Comp. Eng. Math., 9:3 (2022), 30–38
Citation in format AMSBIB
\Bibitem{Gon22}
\by N.~S.~Goncharov
\paper The Poisson equation with Wentzell boundary conditions in the square
\jour J. Comp. Eng. Math.
\yr 2022
\vol 9
\issue 3
\pages 30--38
\mathnet{http://mi.mathnet.ru/jcem220}
\crossref{https://doi.org/10.14529/jcem220303}
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