@article{Du2023, 
author = {Yihong Du and Wenjie Ni},
title = {The Fisher-KPP nonlocal diffusion equation with free boundary and radial symmetry in  R3},
year = {2023},
journal = {Mathematics in Engineering},
volume = {5},
number = {2},
pages = {1-26},
keywords = {nonlocal diffusion, free boundary, spreading rate},
url = {https://www.sciopen.com/article/10.3934/mine.2023041},
doi = {10.3934/mine.2023041},
abstract = {This paper is concerned with the radially symmetric Fisher-KPP nonlocal diffusion equation with free boundary in dimension 3. For arbitrary dimension  N≥2, in [18], we have shown that its long-time dynamics is characterised by a spreading-vanishing dichotomy; moreover, we have found a threshold condition on the kernel function that governs the onset of accelerated spreading, and determined the spreading speed when it is finite. In a more recent work [19], we have obtained sharp estimates of the spreading rate when the kernel function  J(|x|) behaves like  |x|−β as  |x|→∞ in  RN ( N≥2). In this paper, we obtain more accurate estimates for the spreading rate when  N=3, which employs the fact that the formulas relating the involved kernel functions in the proofs of [19] become particularly simple in dimension  3.}
}