Two-Scale Convergence On Periodic Surfaces And Applications

This paper is concerned with the homogenization of model problems in periodic porous media when important phenomena occur on the boundaries of the pores. To this end, we generalize the notion of two-scale convergence for sequences of functions which are deened on periodic surfaces. We apply our results to two model problems : the rst one is a diiusion equation in a porous medium with a Fourier boundary condition, the second one is a coupled system of diiusion equations inside and on the boundaries of the pores of a porous medium.