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 Chelyab. Fiz.-Mat. Zh., 2017, Volume 2, Issue 3, Pages 266–281 (Mi chfmj62)

Mathematics

Asymptotics of a boundary-value problem solution for the Laplace equation with type changing of the boundary condition on two small sites

A. A. Ershova, M. I. Rusanovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
b Chelyabinsk State University, Chelyabinsk, Russia

Abstract: We consider a harmonic function in a three-dimensional bounded domain. The normal derivative is given on almost the entire boundary, excepting two small sections, on which the value of the function itself is specified. For such a harmonic function, by the method of matching asymptotic expansions, a two-scale asymptotics with respect to a small parameter characterizing the size of the mentioned boundary sections is constructed and justified. The physical application of the obtained decomposition is given.

Keywords: boundary value problem, Laplace equation, asymptotic expansion, mixed problem, small parameter, matching method, electrical resistance.

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Citation: A. A. Ershov, M. I. Rusanova, “Asymptotics of a boundary-value problem solution for the Laplace equation with type changing of the boundary condition on two small sites”, Chelyab. Fiz.-Mat. Zh., 2:3 (2017), 266–281

Citation in format AMSBIB
\Bibitem{ErsRus17} \by A.~A.~Ershov, M.~I.~Rusanova \paper Asymptotics of a boundary-value problem solution for the Laplace equation with type changing of the boundary condition on two small sites \jour Chelyab. Fiz.-Mat. Zh. \yr 2017 \vol 2 \issue 3 \pages 266--281 \mathnet{http://mi.mathnet.ru/chfmj62} \elib{https://elibrary.ru/item.asp?id=30487861} 

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