The dynamics of a Fisher-KPP nonlocal diffusion model with free boundaries
Analysis of PDEs
2018-10-11 v2
Abstract
We introduce and study a class of free boundary models with "nonlocal diffusion", which are natural extensions of the free boundary models in Du and Lin [17] and elsewhere, where "local diffusion" is used to describe the population dispersal, with the free boundary representing the spreading front of the species. We show that this nonlocal problem has a unique solution defined for all time, and then examine its long-time dynamical behavior when the growth function is of Fisher-KPP type. We prove that a spreading-vanishing dichotomy holds, though for the spreading-vanishing criteria significant differences arise from the well known local diffusion model in Du and Lin [17].
Keywords
Cite
@article{arxiv.1805.04804,
title = {The dynamics of a Fisher-KPP nonlocal diffusion model with free boundaries},
author = {Jiafeng Cao and Yihong Du and Fang Li and Wantong Li},
journal= {arXiv preprint arXiv:1805.04804},
year = {2018}
}