Singular perturbation of the fourth order elliptic equation when the limit equation is elliptic-parabolic
type: Item
instance of: scholarly article
title: Singular perturbation of the fourth order elliptic equation when the limit equation is elliptic-parabolic
zbMATH Open document ID: 0754.35031
DOI: 10.1007/BF02018071
author: Zongchi Lin
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1992-09-27T00:00:00Z
review text: (From author's summary.) In this paper the author considers the singular perturbation of the fourth order elliptic equation \[ -\varepsilon^ 2 \Delta^ 2 u+y^ m{\partial^ 2u \over\partial y^ 2}+{\partial^ 2 u\over\partial x^ 2}+a(x,y){\partial u\over\partial y}+b(x,y){\partial u\over\partial x}+c(x,y)=0, \] when the limit equation is elliptic- parabolic, where \(\varepsilon\) is a positive parameter, \(m\) is a positive number, \(\Delta\) is the Laplace operator, \(a,b,c\) are sufficiently smooth. Under an appropriate condition applying a boundary layer function, he derives at the sufficient condition of solvability and proves the existence of a solution and gives a uniformly valid asymptotic solution of arbitrary order.
Mathematics Subject Classification ID: 35J35
Mathematics Subject Classification ID: 35B25
zbMATH DE Number: 61725
zbMATH Keywords: boundary layer function
reviewed by: Yukiyoshi Ebihara
MaRDI profile type: Publication
cites work: A Variational Approach to Singularly Perturbed Boundary Value Problems for Ordinary and Partial Differential Equations with Turning Points
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description: scientific article; zbMATH DE number 61725