Non-classical boundary layers for fourth-order equations with singular limit solution
type: Item
instance of: scholarly article
title: Non-classical boundary layers for fourth-order equations with singular limit solution
zbMATH Open document ID: 1021.35026
author: Makram Hamouda
published in: Differential and Integral Equations
publication date: 2002-12-10T00:00:00Z
review text: The author deals with the following fourth order linear model \[ \begin{cases} \varepsilon\Delta^2u^\varepsilon + u^\varepsilon=H\quad \text{in }\Omega,\\ u^\varepsilon=\phi_0,\quad \frac{\partial u^\varepsilon}{\partial\nu} = \phi_1\quad \text{on }\Gamma,\end{cases}\tag{1} \] where \(\phi_0\) and \(\phi_1\) are two given (smooth) functions, \(\Omega\) is a channel of \(\mathbb{R}^3\) and \(H\) is the Heaviside function in the direction orthogonal to the walls (\(z\)-direction). In the \(x\) and \(y\) directions the boundary condition is periodic for \(u^\varepsilon\). The author derives the first-order term in the asymptotic expansion of \(u^\varepsilon\) with respect to \(\varepsilon\).
Mathematics Subject Classification ID: 35C20
Mathematics Subject Classification ID: 35J40
Mathematics Subject Classification ID: 35R05
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35A20
zbMATH DE Number: 1839884
zbMATH Keywords: first-order term
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1839884