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Ufimsk. Mat. Zh., 2015, Volume 7, Issue 3, Pages 16–28 (Mi ufa287)  

This article is cited in 2 scientific papers (total in 2 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

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.

Full text: PDF file (250 kB)
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English version:
Ufa Mathematical Journal, 2015, 7:3, 15–27 (PDF, 218 kB); https://doi.org/10.13108/2015-7-3-15

Bibliographic databases:

UDC: 537.311.3+517.95
MSC: 35J05, 35J25, 35B40, 78M35
Received: 15.04.2015

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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\by R.~R.~Gadylshin, A.~A.~Ershov, S.~V.~Repyevsky
\paper On asymptotic formula for electric resistance of conductor with small contacts
\jour Ufimsk. Mat. Zh.
\yr 2015
\vol 7
\issue 3
\pages 16--28
\mathnet{http://mi.mathnet.ru/ufa287}
\elib{https://elibrary.ru/item.asp?id=24716948}
\transl
\jour Ufa Math. J.
\yr 2015
\vol 7
\issue 3
\pages 15--27
\crossref{https://doi.org/10.13108/2015-7-3-15}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84959041529}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Ershov, “Contact resistance of a square contact”, Proc. Steklov Inst. Math. (Suppl.), 303, suppl. 1 (2018), 70–78  mathnet  crossref  crossref  isi  elib
    2. A. A. Ershov, M. I. Rusanova, “Asimptotika resheniya kraevoi zadachi dlya uravneniya Laplasa so smenoi tipa granichnogo usloviya na dvukh malykh uchastkakh”, Chelyab. fiz.-matem. zhurn., 2:3 (2017), 266–281  mathnet  elib
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