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 Trudy Inst. Mat. i Mekh. UrO RAN, 2012, Volume 18, Number 2, Pages 92–107 (Mi timm811)

Asymptotic expansion of the Dirichlet problem with Laplace equation outside a thin disk

A. A. Ershov

Chelyabinsk State University

Abstract: A uniform asymptotic expansion is found for the exterior Dirichlet problem with Laplace equation outside a thin disk in three-dimensional space. The small parameter is the thickness of the disk. The asymptotic coefficients are constructed by means of the matching method up to solutions of boundary value problems. Near the edges of the disk, the coefficients are presented as series of special functions without specifying the explicit form of the coefficients at the functions. However, it is proved that there exist some coefficients independent of the small parameter.

Keywords: boundary value problem, Laplace equation, asymptotic expansion, thin disk.

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Document Type: Article
UDC: 517.955.8

Citation: A. A. Ershov, “Asymptotic expansion of the Dirichlet problem with Laplace equation outside a thin disk”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 2, 2012, 92–107

Citation in format AMSBIB
\Bibitem{Ers12} \by A.~A.~Ershov \paper Asymptotic expansion of the Dirichlet problem with Laplace equation outside a~thin disk \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2012 \vol 18 \issue 2 \pages 92--107 \mathnet{http://mi.mathnet.ru/timm811} \elib{http://elibrary.ru/item.asp?id=17736189} 

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This publication is cited in the following articles:
1. A. A. Ershov, “Asimptotika resheniya vtoroi kraevoi zadachi dlya uravneniya Laplasa vne maloi okrestnosti otrezka”, Tr. IMM UrO RAN, 21, no. 1, 2015, 81–96
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