RUS  ENG
Full version
JOURNALS // Chelyabinskiy Fiziko-Matematicheskiy Zhurnal // Archive

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.

Received: 15.08.2017
Revised: 15.10.2017



Bibliographic databases:


© Steklov Math. Inst. of RAS, 2024