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Reactive transport through an array of cells with semi-permeable membranes. (English) Zbl 0824.76083
The homogenization method is applied to a problem of diffusion, convection, and nonlinear chemical reactions in a periodic array of solids surrounded by a viscous incompressible fluid. On the interface between the fluid and solid part the authors postulate the continuity of the flux and additional, in general nonlinear, transmission conditions. In the limit process as the number of solids tends to infinity and at the same time their size tends to zero while the solids concentration remains fixed, the model equations of the microprocess are solved. The convergence result of the microscopic solution towards a macroscopic one is obtained. The limit problem is a nonlinearly coupled problem with two scales, a global and a local one. In this frame the recently developed technique of two-scale convergence is used.
Reviewer: Th.Lévy (Paris)

MSC:
76S05 Flows in porous media; filtration; seepage
76V05 Reaction effects in flows
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
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