Global dynamics and spectrum comparison of a reaction-diffusion system with mass conservation

TL;DR

This paper analyzes the long-term behavior of a mass-conserving reaction-diffusion system related to cell polarity, establishing global existence, stability, and instability of solutions, and comparing spectral properties.

Contribution

It provides the first comprehensive analysis of global dynamics and spectrum comparison for a reaction-diffusion system with mass conservation in the context of cell polarity.

Findings

Proved global-in-time existence of solutions.

Identified conditions for stability and instability of stationary solutions.

Compared spectral properties of the system.

Abstract

We study global-in-time behavior of the solution to a reaction-diffusion system with mass conservation, as proposed in the study of cell polarity, particularly, the second model of \cite{oi07}. First, we show global-in-time existence of solution with compact orbit and then we examine stability and instability of stationary solutions.}{Reaction diffusion system; mass conservation; cell polarity; global-in-time behavior; Lyapunov function.