This article is cited in 6 papers

Asymptotic behaviour of solutions of a singular elliptic system in a rectangle

A. R. Danilin

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: A system of two conjugate elliptic equations with a small parameter at the highest derivatives is considered in a rectangle with two sides parallel to the characteristics of the limiting equations.
The method of matched asymptotic expansions is used for the construction of uniform asymptotic series for solutions of this system up to an arbitrary power of the small parameter.

UDC: 517.977

MSC: 35J65, 35B40, 35C20

Received: 22.02.2001 and 20.06.2002

DOI: 10.4213/sm705

 English version: Sbornik: Mathematics, 2003, 194:1, 31–61

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