Open Access
Translator Disclaimer
2013 Analysis of Mixed Elliptic and Parabolic Boundary Layers with Corners
Gung-Min Gie, Chang-Yeol Jung, Roger Temam
Int. J. Differ. Equ. 2013(SI2): 1-13 (2013). DOI: 10.1155/2013/532987


We study the asymptotic behavior at small diffusivity of the solutions,uε, to a convection-diffusion equation in a rectangular domain . The diffusiveequation is supplemented with a Dirichlet boundary condition, which is smoothalong the edges and continuous at the corners. To resolve the discrepancy, on , between uε and the corresponding limit solution, u0, we propose asymptotic expansionsof uε at any arbitrary, but fixed, order. In order to manage some singulareffects near the four corners of , the so-called elliptic and ordinary corner correctorsare added in the asymptotic expansions as well as the parabolic and classicalboundary layer functions. Then, performing the energy estimates on the differenceof uε and the proposed expansions, the validity of our asymptotic expansions isestablished in suitable Sobolev spaces.


Download Citation

Gung-Min Gie. Chang-Yeol Jung. Roger Temam. "Analysis of Mixed Elliptic and Parabolic Boundary Layers with Corners." Int. J. Differ. Equ. 2013 (SI2) 1 - 13, 2013.


Received: 27 January 2013; Accepted: 1 April 2013; Published: 2013
First available in Project Euclid: 24 January 2017

zbMATH: 1272.35094
MathSciNet: MR3055164
Digital Object Identifier: 10.1155/2013/532987

Rights: Copyright © 2013 Hindawi


Vol.2013 • No. SI2 • 2013
Back to Top