Uniqueness and global stability of forced waves in a shifting environment

Abstract

This paper deals with the uniqueness and global stability of forced extinction waves for the nonlocal dispersal Fisher-KPP equation in a shifting environment where the favorable habitat is shrinking. Specifically, we first obtain the uniqueness by using the sliding technique and then establish the global exponential stability via the monotone semiflows approach combined with the method of super- and subsolutions. Our developed arguments can also be used to prove the same conclusion for the corresponding random diffusion problem.