Fast reaction limit of reaction-diffusion systems

TL;DR

This paper rigorously analyzes the singular reaction limit of general reaction-diffusion systems, deriving the limit equations and providing a comprehensive mathematical framework applicable across various scientific fields.

Contribution

It introduces a unified approach to the singular limit problem for reaction-diffusion systems, extending previous specific cases to a general setting.

Findings

Derived the limit equations for reaction-diffusion systems in the singular reaction regime

Established a rigorous mathematical theory for the reaction limit

Unified framework applicable to multiple scientific disciplines

Abstract

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.