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Homogenization in chemical reactive flows. (English) Zbl 1195.35037

Summary: This paper concerns the homogenization of two nonlinear models for chemical reactive flows through the exterior of a domain containing periodically distributed reactive solid grains (or reactive obstacles). In the first model, the chemical reactions take place on the walls of the grains, while in the second one the fluid penetrates the grains and the reactions take place therein. The effective behavior of these reactive flows is described by a new elliptic boundary-value problem containing an extra zero-order term which captures the effect of the chemical reactions.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35Q35 PDEs in connection with fluid mechanics
76M50 Homogenization applied to problems in fluid mechanics
76V05 Reaction effects in flows
80A32 Chemically reacting flows
35J25 Boundary value problems for second-order elliptic equations
35J86 Unilateral problems for linear elliptic equations and variational inequalities with linear elliptic operators
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