Abstract
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 where the heterogeneities are not arranged in a strictly periodic manner. The result is a two-scale model formulated in x-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, $L^\infty$-bounds, uniqueness, energy inequality) are obtained in $x$-dependent Bochner spaces.
Original language | English |
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Pages (from-to) | 493-516 |
Journal | European Journal of Applied Mathematics |
Volume | 22 |
Issue number | 5 |
DOIs | |
Publication status | Published - 2011 |