Nonlinear effects for flow in periodically constricted channel caused by high injection rate

We consider a stationary viscous incompressible how through a periodically constricted channel with the period and thickness epsilon, governed by a strong injection of order epsilon(-1). We prove the well-posedness of the homogenized problem and the convergence of the homogenization process. We obtain a nonlinear filtration law and we give the Taylor expansion of the filtration velocity as a function of the pressure gradient.