Boundary layer behavior in perturbed second-order systems
type: Item
instance of: scholarly article
title: Boundary layer behavior in perturbed second-order systems
zbMATH Open document ID: 0558.34046
DOI: 10.1016/0022-247X(84)90011-8
author: F. A. Howes
published in: Journal of Mathematical Analysis and Applications
publication date: 1984-01-01T00:00:00Z
review text: We present here some results on the asymptotic behavior as \(\epsilon \to 0^+\) of solutions of the Dirichlet problem for the singularly perturbed second-order system in \({\mathbb{R}}^ n\) \({\mathcal E}y''={\mathcal F}(y)y'+g(x,y)\), \(a<x<b\), where \({\mathcal F}\) is an (n\(\times n)\)-matrix valued function. In particular, we are interested in providing sufficient conditions in order that a solution of this problem display boundary layer behavior at an endpoint \((x=a\) or \(x=b)\). Layer behavior simply means nonuniform dependence of the solution on x and \({\mathcal E}\) as \({\mathcal E}\to 0^+\), and very often it is this nonuniform or singular dependence which affords the most insight into natural phenomena modelled by the system.
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34D15
zbMATH DE Number: 3889957
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: singularly perturbed second-order system
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3889957