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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2013, Volume 53, Number 11, Pages 1768–1783
DOI: https://doi.org/10.7868/S0044466913110045 (Mi zvmmf9940) 		 
Asymptotics of the solution of Laplace’s equation with third-type boundary conditions on the boundaries of two small holes

S. R. Garifullinaa, E. Yu. Postnikovab

a Bashkir State University, ul. Zaki Validi 32, Ufa, 450074, Bashkortostan, Russia
b Chelyabinsk State University, ul. Brat'ev Kashirinykh 129, Chelyabinsk, 454001, Russia
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DOI: https://doi.org/10.7868/S0044466913110045
Abstract: A boundary value problem for Laplace’s equation in a bounded domain with two small holes is considered. Third-type boundary conditions are set on the boundaries of the holes. A Neumann condition is specified on the outer boundary of the domain. A uniform asymptotic approximation of the solution is constructed and justified up to an arbitrary power of a small parameter.
Key words: asymptotic expansion, small parameter, boundary value problem for Laplace’s equation, method of matched asymptotic expansions.
Received: 20.05.2013
English version:
Computational Mathematics and Mathematical Physics, 2013, Volume 53, Issue 11, Pages 1591–1606
DOI: https://doi.org/10.1134/S0965542513110043
Bibliographic databases:
Document Type: Article
UDC: 519.632.4
Language: Russian
Citation: S. R. Garifullina, E. Yu. Postnikova, “Asymptotics of the solution of Laplace’s equation with third-type boundary conditions on the boundaries of two small holes”, Zh. Vychisl. Mat. Mat. Fiz., 53:11 (2013), 1768–1783; Comput. Math. Math. Phys., 53:11 (2013), 1591–1606
Citation in format AMSBIB
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    		Æóðíàë âû÷èñëèòåëüíîé ìàòåìàòèêè è ìàòåìàòè÷åñêîé ôèçèêè Computational Mathematics and Mathematical Physics
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