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Ufa Mathematical Journal, 2015, Volume 7, Issue 3, Pages 15–27
DOI: https://doi.org/10.13108/2015-7-3-15 (Mi ufa287) 		 
This article is cited in 4 scientific papers (total in 4 papers)

On asymptotic formula for electric resistance of conductor with small contacts

R. R. Gadylshina, A. A. Ershovb, S. V. Repyevskyb

a Bashkir State Pedagogical University, Ufa, Russia
b Chelyabinsk State University, Chelyabinsk, Russia
English version PDF (218 kB) Citations (4)
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DOI: https://doi.org/10.13108/2015-7-3-15
Abstract: We construct and justify rigorously the complete asymptotic expansion for the electric resistance of a three-dimensional resistance connected by two small contacts of arbitrary shape. We obtain explicit formulae for the first two terms in the asymptotics generalized the classical Helm formula of one-term asymptotics for two small round contacts of same radius.
Keywords: electrical resistance, small contacts, Helm formula, asymptotic expansion, boundary value problem, the method of matching asymptotic expansions, Laplace equation, mixed problem.
Received: 15.04.2015
Russian version:
Ufimskii Matematicheskii Zhurnal, 2015, Volume 7, Issue 3, Pages 16–28
Bibliographic databases:
Document Type: Article
UDC: 537.311.3+517.95
MSC: 35J05, 35J25, 35B40, 78M35
Language: English
Original paper language: Russian
Citation: R. R. Gadylshin, A. A. Ershov, S. V. Repyevsky, “On asymptotic formula for electric resistance of conductor with small contacts”, Ufimsk. Mat. Zh., 7:3 (2015), 16–28; Ufa Math. J., 7:3 (2015), 15–27
Citation in format AMSBIB
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  • https://doi.org/10.13108/2015-7-3-15
  • https://www.mathnet.ru/eng/ufa/v7/i3/p16
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Уфимский математический журнал
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    Russian version PDF:155
    English version PDF:23
    References:64
     
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