Fast reaction limit of reaction-diffusion systems

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.