Persistence and Extinction of Nonlocal Dispersal Evolution Equations in Moving Habitats

Abstract

This paper is devoted to the study of persistence and extinction of a species modeled by nonlocal dispersal evolution equations in moving habitats with moving speed $c$. It is shown that the species becomes extinct if the moving speed $c$ is larger than the so called spreading speed $c^{\ast }$, where $c^{\ast }$ is determined by the maximum linearized growth rate function. If the moving speed $c$ is smaller than $c^{\ast }$, it is shown that the persistence of the species depends on the patch size of the habitat, namely, the species persists if the patch size is greater than some number $L^{\ast }$ and in this case, there is a traveling wave solution with speed $c$, and it becomes extinct if the patch size is {smaller} than $L^{\ast }$.

References in corpus (1)

• On a simple criterion for the existence of a principal eigenfunction of some nonlocal operators