2018/05/13 by Jia-Feng Cao, Cao, Jiafeng, Yihong Du +5
Mathematics · Medicine · Physics and Astronomy · #35K57 #35R20 #92D25 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1805.04804
openalex publication_date 2018/05/13 · openalex created_date 2018/05/17 · openalex updated_date 2026/07/28
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].