Pushed fronts of monostable reaction-diffusion-advection equations

TL;DR

This paper investigates the behavior and stability of pushed fronts in monostable reaction-diffusion-advection equations, establishing their exponential approach to unstable states and confirming their stability.

Contribution

It provides new proofs of exponential behavior and stability of pushed fronts in periodic reaction-diffusion equations with general monostable nonlinearities.

Findings

Exponential decay of pushed fronts near unstable states

Exponential behavior of pulsating fronts with speeds above minimal

Proof of stability for pushed fronts

Abstract

In this paper, we prove some qualitative properties of pushed fronts for the periodic reaction-diffusion-equation with general monostable nonlinearities. Especially, we prove the exponential behavior of pushed fronts when they are approaching their unstable state. The proof also allows us to get the exponential behavior of pulsating fronts with speed $c$ larger than the minimal speed. Through the exponential behavior, we finally prove the stability of pushed fronts.