The corner boundary layer in nonlinear singularly perturbed elliptic equations.
type: Item
instance of: scholarly article
title: The corner boundary layer in nonlinear singularly perturbed elliptic equations.
zbMATH Open document ID: 1114.35304
author: I. V. Denisov
published in: Computational Mathematics and Mathematical Physics
publication date: 2003-07-01T00:00:00Z
review text: In this paper the author analyzes the possibility of constructing an asymptotic expansion of the solution to the Dirichlet problem for the elliptic equation \({\varepsilon}^2{\Delta}u=F(u,x,y,\epsilon)\) defined on a rectangle. As compared to previous studies, the analysis is performed without two restrictions, which means that it applies to arbitrary nonlinear functions \(F(u,x,y,\varepsilon)\). The main result consist in the construction of the corner part of an asymptotic solution to the boundary value problem.
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35C20
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 1940687
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: elliptic equation
zbMATH Keywords: asymptotic expansion
zbMATH Keywords: solution
zbMATH Keywords: singularly perturbed
zbMATH Keywords: nonlinear
reviewed by: A. Tret'yakov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1940687