Differential and Integral Equations

Non-classical boundary layers for fourth-order equations with singular limit solution

Makram Hamouda

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Abstract

In this article we study non classical singular perturbation problems involving boundary layers in the interior of the domain. As usual, these problems contain a small parameter which produces, when this parameter approaches zero, classical boundary layers located at the boundary. If we moreover consider a singular source function, we produce also boundary layers inside the domain. Our aim in this article is to study this kind of boundary layers. We consider, here, a model with a fourth-order differential operator, and the open set is a channel to avoid the technicalities due to the curvature of the boundary. Other stationary problems and time dependent problems will be considered elsewhere.

Article information

Source
Differential Integral Equations, Volume 15, Number 12 (2002), 1435-1458.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060706

Mathematical Reviews number (MathSciNet)
MR1920254

Zentralblatt MATH identifier
1021.35026

Subjects
Primary: 35B25: Singular perturbations
Secondary: 34E15: Singular perturbations, general theory 35C20: Asymptotic expansions 35J40: Boundary value problems for higher-order elliptic equations 35R05: Partial differential equations with discontinuous coefficients or data

Citation

Hamouda, Makram. Non-classical boundary layers for fourth-order equations with singular limit solution. Differential Integral Equations 15 (2002), no. 12, 1435--1458. https://projecteuclid.org/euclid.die/1356060706


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