R. R. Gadylshin, A. A. Ershov, S. V. Repyevsky, “On asymptotic formula for electric resistance of conductor with small contacts”, Ufimsk. Mat. Zh., 2015, Volume 7, Issue 3,Pages <nobr>16

This article is cited in 4 papers

On asymptotic formula for electric resistance of conductor with small contacts

R. R. Gadylshin^a, A. A. Ershov^b, S. V. Repyevsky^b

^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.

UDC: 537.311.3+517.95

MSC: 35J05, 35J25, 35B40, 78M35

Received: 15.04.2015