Convection-diffusion equations in a circle: the compatible case
type: Item
instance of: scholarly article
title: Convection-diffusion equations in a circle: the compatible case
zbMATH Open document ID: 1228.35021
author: C. Jung
author: R. Temam
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2011-07-19T00:00:00Z
review text: The authors consider the following 2D singular perturbation problem \[ \begin{cases}-\varepsilon \Delta u^{\varepsilon}-\partial_y u^{\varepsilon}=f(x,y) &\text{in } D,\\ u^{\varepsilon}=0 &\text{on } \partial D,\end{cases}\tag{E} \] where \(D\) is the unit disc \(D=\{(x,y): x^2+y^2\leq 1\}\). They study the convergence of the family \(u^{\varepsilon}\) when \(\varepsilon\rightarrow 0\). As the points \((\pm 1,0)\) are characteristic for the limit problem, the boundary-layer estimates require special study near these points. The authors prove various convergence results and corrector formulas depending on the degree of compatibility conditions on the data at these characteristic points.
reviewed by: Bernard Ducomet
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 76R50
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 5925831
zbMATH Keywords: boundary layers
zbMATH Keywords: characteristic points
zbMATH Keywords: compatibility conditions
zbMATH Keywords: corrector formulas
MaRDI profile type: Publication
full work available at URL: j.matpur.2011.03.006
OpenAlex ID: W2008169430
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DOI: 10.1016/J.MATPUR.2011.03.006
description: scientific article; zbMATH DE number 5925831