Analysis of mixed elliptic and parabolic boundary layers with corners
type: Item
instance of: scholarly article
title: Analysis of mixed elliptic and parabolic boundary layers with corners
zbMATH Open document ID: 1272.35094
DOI: 10.1155/2013/532987
author: Gung-Min Gie
author: C. Jung
author: R. Temam
published in: International Journal of Differential Equations
publication date: 2013-06-10T00:00:00Z
review text: Summary: We study the asymptotic behavior at small diffusivity of the solutions, \(u^\varepsilon\), to a convection-diffusion equation in a rectangular domain \(\Omega\). The diffusive equation is supplemented with a Dirichlet boundary condition, which is smooth along the edges and continuous at the corners. To resolve the discrepancy on \(\partial \Omega\) between \(u^\varepsilon\) and the corresponding limit solution, \(u^0\), we propose asymptotic expansions of \(u^\varepsilon\) at any arbitrary, but fixed, order. In order to manage some singular effects near the four corners of \(\Omega\), the so-called elliptic and ordinary corner correctors are added in the asymptotic expansions as well as the parabolic and classical boundary layer functions. Then, performing the energy estimates on the difference of \(u^\varepsilon\) and the proposed expansions, the validity of our asymptotic expansions is established in suitable Sobolev spaces.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 6172133
Wikidata QID: Q58923608
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/532987
OpenAlex ID: W2133388669
cites work: Asymptotic Analysis of a Singular Perturbation Problem
cites work: Q4039929
cites work: Q3276453
cites work: Differentiability of Solutions to Hyperbolic Initial Boundary Value Problems
cites work: Smooth solutions of the heat and wave equations
cites work: Behaviour at time t=0 of the solutions of semi-linear evolution equations
cites work: Numerical Resolution Near t = 0 of Nonlinear Evolution Equations in the Presence of Corner Singularities in Space Dimension 1
cites work: Accurate numerical resolution of transients in initial-boundary value problems for the heat equation
cites work: On the Nature of Initial-Boundary Value Solutions for Dispersive Equations
cites work: Asymptotic expansion of the Stokes solutions at small viscosity: the case of non-compatible initial data
cites work: Q3792860
cites work: Q5487623
cites work: Boundary layers in smooth curvilinear domains: parabolic problems
cites work: Q5187597
description: scientific article; zbMATH DE number 6172133