Pushed fronts of monostable reaction-diffusion-advection equations

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.(c) 2023 Elsevier Inc. All rights reserved.

Automated summary

In this paper, we demonstrate the qualitative properties of pushed fronts for the periodic reaction-diffusion equation with general monostable nonlinearities. Specifically, we prove the exponential behavior of pushed fronts as they approach the unstable state. Our proof also enables us to determine the exponential behavior of pulsating fronts with speeds greater than the minimal speed. Ultimately, through the exponential behavior, we establish the stability of pushed fronts.