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A model of filtration in a multispecies porous medium with mechanical and chemical interaction between the flow and the porous matrix is presented. The species removed by the medium are transported either as solids or as solutes. The accumulation of the migrating particles in proximity of the outflow surface gives rise to the growth of a compact layer, with high hydraulic resistance. The corresponding mathematical problem is a free boundary problem for parabolic and hyperbolic partial differential equations. Existence and uniqueness globally in time are proved.
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Fasano et al. (2000) studied this question.
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