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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2013, Volume 53, Number 7, Pages 1094–1106
DOI: https://doi.org/10.7868/S0044466913070089 (Mi zvmmf9822) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Mixed problem for a harmonic function

A. A. Ershov

Chelyabinsk State University
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DOI: https://doi.org/10.7868/S0044466913070089
Abstract: A harmonic function is considered in a three-dimensional bounded domain. Its normal derivative is given on nearly the entire boundary of the domain, while the value of the harmonic function is specified on the remaining small portion. The method of matched asymptotic expansions is used to construct a complete uniform asymptotic expansion of the function in powers of a small parameter characterizing the size of the boundary portion with a specified function value. The asymptotic expansion is rigorously substantiated.
Key words: harmonic function, mixed boundary value problem, small parameter, method of matched asymptotic expansions.
Received: 14.02.2013
English version:
Computational Mathematics and Mathematical Physics, 2013, Volume 53, Issue 7, Pages 908–919
DOI: https://doi.org/10.1134/S0965542513070087
Bibliographic databases:
Document Type: Article
UDC: 519.632.4
Language: Russian
Citation: A. A. Ershov, “Mixed problem for a harmonic function”, Zh. Vychisl. Mat. Mat. Fiz., 53:7 (2013), 1094–1106; Comput. Math. Math. Phys., 53:7 (2013), 908–919
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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