The Fisher-KPP nonlocal diffusion equation with free boundary and radial symmetry in R3

Author(s)
Du, Yihong
Ni, Wenjie
Publication Date
2022-06-16
Abstract
<p>This paper is concerned with the radially symmetric Fisher-KPP nonlocal diffusion equation with free boundary in dimension 3. For arbitrary dimension <i>N</i> ≥ 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|<sup><i>−β</i></sup> as |x| → ∞ in R<sup><i>N</i></sup> (<i>N</i> ≥ 2). In this paper, we obtain more accurate estimates for the spreading rate when <i>N</i> = 3, which employs the fact that the formulas relating the involved kernel functions in the proofs of [19] become particularly simple in dimension 3.</p>
Citation
Mathematics in Engineering, 5(2), p. 1-26
ISSN
2640-3501
Link
Publisher
AIMS Press
Rights
Attribution 4.0 International
Title
The Fisher-KPP nonlocal diffusion equation with free boundary and radial symmetry in R3
Type of document
Journal Article
Entity Type
Publication

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