We consider an ε -periodic structure formed by two interwoven and connected components which stand for the fissure system and the porous matrix. We assume that on the matrix-fissure interface the pressure has a jump of order ε −1 with respect to the fluid flux which is continuous. We prove that the corresponding homogenized system is exactly that proposed by Barenblatt and al. [1].
Mathematics Subject Classification (2000). 35B27, 76R50, 76S05.
International audienceWe study the homogenization of a diffusion process which takes place in a binary structure formed by an ambiental connected phase surrounding a suspension of very small particles of general form distributed in an $\varepsilon$-periodic network. The asymptotic distribution of the concentration is determined for both phases, as $\varepsilon\to 0$, assuming that the suspension has mass of unity order and vanishing volume. Three cases are distinguished according to the values of a certain rarefaction number. When it is positive and finite, the macroscopic system involves a two-concentration system, coupled through a term accounting for the non local effects. In the other two cases, where the rarefaction number is either infinite or going to zero, although the form of the system is much simpler, some peculiar effects still account for the presence of the suspension
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