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 $c^*$, where $c^*$ is determined by the maximum linearized growth rate function. If the moving speed $c$ is smaller than $c^*$, 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 $L^*$ and in this case, there is a traveling wave solution with speed $c$, and it becomes extinct if the patch size is {smaller} than $L^*$.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2019
- DOI:
- 10.48550/arXiv.1906.07881
- arXiv:
- arXiv:1906.07881
- Bibcode:
- 2019arXiv190607881D
- Keywords:
-
- Mathematics - Dynamical Systems