Steady and evolution Stokes equations in a porous media [medium] with nonhomogeneous boundary data: a homogenization process
A. K. Nandakumar · Differential and Integral Equations · 1992
In this paper, we study the homogenization of the steady state and evolution Stokes equations with nonhomogeneous Dirichlet data on the boundary of the holes of a porous median~, obtained from a domain n by removing a large number of holes of size c: (c: > 0, a small parameter), periodically distributed with period c:.In the homogenization process, we obtain a well defined system of equations involving both the 'slow' variable x and the 'fast' variable y = .!..We also derive the Darcy's law which contains an extra term and this additional term is the contribution due to the non-homogeneous data.