Stability of Single Transition Layer in Mass-Conserving Reaction-Diffusion Systems with Bistable Nonlinearity

TL;DR

This paper investigates the existence and stability of single transition layer solutions in mass-conserving reaction-diffusion systems with bistable nonlinearity, using singular perturbation theory and Evans function analysis.

Contribution

It establishes conditions for the existence and stability of stationary solutions with a single internal transition layer in such systems.

Findings

Existence of stationary single transition layer solutions proven.

A stability criterion based on Evans function is derived.

Analytical methods applicable to general assumptions in mass-conserving systems.

Abstract

Mass-conserving reaction-diffusion systems with bistable nonlinearity are considered under general assumptions. The existence of stationary solutions with a single internal transition layer in such reaction-diffusion systems is shown using the analytical singular perturbation theory. Moreover, a stability criterion for the stationary solutions is provided by calculating the Evans function.