Initial-Boundary Layer Associated with the Nonlinear Darcy-Brinkman System
Abstract
We study the interaction of initial layer and boundary layer in the nonlinear Darcy-Brinkman system in the vanishing Darcy number limit. In particular, we show the existence of a function of corner layer type (so-called initial-boundary layer) in the solution of the nonlinear Darcy-Brinkman system. An approximate solution is constructed by the method of multiple scale expansion in space and in time. We establish the optimal convergence rates in various Sobolev norms via energy method.
Recommended Citation
D. Han and X. Wang, "Initial-Boundary Layer Associated with the Nonlinear Darcy-Brinkman System," Journal of Differential Equations, vol. 256, no. 2, pp. 609 - 639, Elsevier, Jan 2014.
The definitive version is available at https://doi.org/10.1016/j.jde.2013.09.014
Department(s)
Mathematics and Statistics
Keywords and Phrases
Boundary layer; Darcy-Brinkman system; Initial layer; Initial-boundary layer; Multiple scale expansion; Vanishing darcy number limit
International Standard Serial Number (ISSN)
0022-0396
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2014 Elsevier, All rights reserved.
Publication Date
01 Jan 2014
Comments
Supported in part by the National Science Foundation, a COFRA award from FSU, and a 111 project from the Chinese Ministry of Education at Fudan University.