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Chelyabinskiy Fiziko-Matematicheskiy Zhurnal, 2017, Volume 2, Issue 3, Pages 266–281
(Mi chfmj62)
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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.
Received: 15.08.2017 Revised: 15.10.2017
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
Linking options:
https://www.mathnet.ru/eng/chfmj62 https://www.mathnet.ru/eng/chfmj/v2/i3/p266
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