Singularly perturbed nonlinear second order elliptic equation
type: Item
instance of: scholarly article
title: Singularly perturbed nonlinear second order elliptic equation
zbMATH Open document ID: 0642.35007
DOI: 10.1007/BF02017404
author: Shan Jin
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1987-01-01T00:00:00Z
review text: The author studies singular perturbation problems of some semilinear second order elliptic equations with nonlinear boundary value conditions \[ \epsilon^ 2\sum_{i,j}\partial /\partial \chi_ i[a_{ij}(\chi,\epsilon)\partial u/\partial \chi_ i- h(\chi,u,\epsilon)]=0\quad (\chi \in \Omega \subset R^ n); \] \[ \beta (\chi,u,\partial u/\partial \ell,\epsilon)=0\quad (\chi \in \partial \Omega) \] where \(\epsilon\) is a small positive parameter and \(\partial u/\partial \ell\) is a directional derivative, which lies on an oblique vector \({\vec \ell}(x,\epsilon)\). He gives a construction of the asymptotic solutions and a proof of their asymptotic correctness, which is based on the principle of contraction mapping.
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35C20
zbMATH DE Number: 4046219
zbMATH Keywords: singular perturbation
zbMATH Keywords: semilinear
zbMATH Keywords: nonlinear boundary value conditions
zbMATH Keywords: oblique vector
zbMATH Keywords: asymptotic solutions
zbMATH Keywords: asymptotic correctness
zbMATH Keywords: principle of contraction
MaRDI profile type: Publication
cites work: Semilinear elliptic boundary value problems with small parameters
cites work: Q5596448
full work available at URL: https://doi.org/10.1007/bf02017404
OpenAlex ID: W1981342434
description: scientific article; zbMATH DE number 4046219