This article is cited in 6 papers

The asymptotics of the solution of an equation with a small parameter in a domain with angular points

E. F. Lelikova

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

Abstract: The asymptotic behaviour of solutions of the first boundary-value problem for a second-order elliptic equation in a domain with angular points is investigated for the case when a small parameter is involved in the equation only as a factor multiplying one of the highest order derivatives and the limit equation is an ordinary differential equation. Although the order of the limit equation coincides with that of the original equation, the problem in question is singularly perturbed. The asymptotic behaviour of the solution of this problem is studied by the method of matched asymptotic expansions.
Bibliography: 11 titles.

Keywords: small parameter, asymptotic behaviour, angular point.

UDC: 517.956

MSC: Primary 35B40; Secondary 35B25

Received: 30.10.2009

DOI: 10.4213/sm7646

 English version: Sbornik: Mathematics, 2010, 201:10, 1495–1510

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