Interface disappearance in fast reaction limit

TL;DR

This paper investigates the fast reaction limit in a two-component system with power-type reaction terms, showing that the initial interface vanishes instantly and solutions converge to the heat equation.

Contribution

It extends the understanding of the fast reaction limit to systems with power reaction terms, demonstrating interface disappearance and convergence to the heat equation.

Findings

Initial interface disappears immediately.

Solutions converge to the heat equation.

Behavior differs from systems with identical reaction terms.

Abstract

We study the singular limit problem referred to as the fast reaction limit. This problem has been extensively studied when the same reaction term is used in a two-component system. However, the behavior of the solution under different reaction terms remains not yet well understood. In this paper, we will consider the problem where the reaction term is represented by a power term. We prove that the initial interface disappears immediately, and the function converges to a solution that satisfies the heat equation.