This article is cited in 5 papers

Corner boundary layer in nonlinear singularly perturbed elliptic problems

I. V. Denisov

Tula State Pedagogical University, pr. Lenina 125, Tula, 300026, Russia

Abstract: The Dirichlet problem in a rectangle is considered for the elliptic equation $\varepsilon^2\Delta u=F(u,x,y,\varepsilon)$, where $F(u,x,y,\varepsilon)$ is a nonlinear function of $u$. The method of corner boundary functions is applied to the problem. Assuming that the leading term of the corner part of the asymptotics exists, an asymptotic expansion of the solution is constructed and the remainder is estimated.

Key words: nonlinear singularly perturbed elliptic problems, asymptotic solution method, corner boundary layer.

UDC: 519.632

Received: 13.11.2006
Revised: 05.07.2007

 English version: Computational Mathematics and Mathematical Physics, 2008, 48:1, 59–75

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