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.