Initial-Boundary Layer Associated with the Nonlinear Darcy-Brinkman System
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.
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
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)
Article - Journal
© 2014 Elsevier, All rights reserved.
01 Jan 2014