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Fast reaction limit of reaction-diffusion systems. (English) Zbl 1462.35035

Summary: Singular limit problems of reaction-diffusion systems have been studied in cases where the effects of the reaction terms are very large compared with those of the other terms. Such problems appear in literature in various fields such as chemistry, ecology, biology, geology and approximation theory. In this paper, we deal with the singular limit of a general reaction-diffusion system including many problems in the literature. We formulate the problem, derive the limit equation and establish a rigorous mathematical theory.

MSC:

35B25 Singular perturbations in context of PDEs
35K51 Initial-boundary value problems for second-order parabolic systems
35K57 Reaction-diffusion equations
35K65 Degenerate parabolic equations
35R35 Free boundary problems for PDEs
80A22 Stefan problems, phase changes, etc.
80A30 Chemical kinetics in thermodynamics and heat transfer
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References:

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