The dynamics of a Fisher-KPP nonlocal diffusion model with free boundaries

By Jia-Feng Cao, Yihong Du, Fang Li, Wan-Tong Li. Journal of Functional Analysis, 2018

137 citations recorded by the source corpus.

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].

Subfields: Applied Mathematics, Mathematical Physics, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/328678af0f97038a9e4a48c6169a1cd37c6d596f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Mingxin Wang
2. Yihong Du
3. Meng Zhao
4. Rui Peng
5. Zongming Guo
6. Yang Zhang
7. Junping Shi
8. Yuan Lou

In Mathematical Physics

1. Mingxin Wang
2. Yihong Du
3. Meng Zhao
4. Rui Peng
5. Zhigui Lin
6. Junping Shi
7. Yang Zhang
8. Chang-Hong Wu

In Public Health, Environmental and Occupational Health

1. Mingxin Wang
2. Yihong Du
3. Meng Zhao
4. Rui Peng
5. Junping Shi
6. Yang Zhang
7. Peter Y. H. Pang
8. Yonggang Zhao

Citations in the corpus

• Two species nonlocal diffusion systems with free boundaries (2019, methodology): “In [6], such a nonlocal diffusion operator was applied to the free boundary model of [8], to investigate the spreading behaviour of a new or invasive species.”