Uniqueness and stability of monostable pulsating fronts for multi-dimensional reaction-diffusion-advection systems in periodic media

Abstract

In this paper, we consider the phenomenon of monostable pulsating fronts for multi-dimensional reaction-diffusion-advection systems in periodic media. Recent results have addressed the existence of pulsating fronts and the linear determinacy of spreading speed (Du, Li and Shen, \textit{J. Funct. Anal.} \textbf{282} (2022) 109415). In the present paper, we investigate the uniqueness and stability of monostable pulsating fronts with nonzero speed. We first derive precise asymptotic behaviors of these fronts as they approach the unstable limiting state. Utilizing these properties, we then prove the uniqueness modulo translation of pulsating fronts with nonzero speed. Furthermore, we show that these pulsating fronts are globally asymptotically stable for solutions of the Cauchy problem with front-like initial data. In particular, we establish the uniqueness and global stability of the critical pulsating front in such systems. These results are subsequently applied to a two-species competition system.