Homogenisation of a locally periodic medium with areas of low and high diffusivity
T.L. van Noorden, Adrian Muntean · European Journal of Applied Mathematics · 2011
We aim at understanding transport in porous materials consisting of regions with both high and low diffusivities. We apply a formal homogenisation procedure to the case wherethe heterogeneities are not arranged in a strictly periodic manner. The result is a two-scale model formulated inx-dependent Bochner spaces. We prove the weak solvability of the limit two-scale model for a prototypical advection–diffusion system of minimal size. A special feature of our analysis is that most of the basic estimates (positivity,L∞-bounds, uniqueness, energy inequality) are obtained in thex-dependent Bochner spaces.