Please use this identifier to cite or link to this item: https://hdl.handle.net/1959.11/56292
Title: The High Dimensional Fisher-KPP Nonlocal Diffusion Equation with Free Boundary and Radial Symmetry, Part 1
Contributor(s): Du, Yihong  (author)orcid ; Ni, Wenjie  (author)orcid 
Publication Date: 2022-06
Early Online Version: 2022-06-28
DOI: 10.1137/21M1451920
Handle Link: https://hdl.handle.net/1959.11/56292
Abstract: 

This is Part 1 of a two-part series, where we study the radially symmetric high dimensional Fisher-KPP nonlocal diffusion equation with free boundary, and obtain a rather complete description of its long-time dynamical behavior, which reveals both similarities and fundamental differences to its one dimensional version considered in [J. Cao, Y. Du, F. Li, and W. T. Li, J. Funct. Anal., 277 (2019), pp. 2772--2814; Y. Du, F. Li, and M. Zhou, J. Math. Pure Appl., 154 (2021), pp. 30--66; Y. Du and W. Ni, Rate of Propagation for the Fisher-KPP Equation with Nonlocal Diffusion, and Free Boundaries, preprint, 2021] recently. Our goals on the long-time dynamics of the model include (a) find the threshold condition on the kernel function that governs the onset of accelerated spreading, (b) determine the spreading speed when it is finite, (c) obtain sharp estimates of the spreading profile for finite speed spreading as well as for accelerated spreading. The tasks in (a) and (b) are carried out here in Part 1, while (c) is done in a separate Part 2. This high dimensional problem poses considerable technical difficulties when the rate of spreading is considered, and we overcome that by introducing an intermediate kernel function which plays a crucial role both in determining the onset condition for accelerated spreading and in obtaining the spreading speed when it is finite.

Publication Type: Journal Article
Grant Details: ARC/DP220101820
Source of Publication: SIAM Journal on Mathematical Analysis, 54(3), p. 3930-3973
Publisher: Society for Industrial and Applied Mathematics
Place of Publication: United State of America
Fields of Research (FoR) 2020: 490410 Partial differential equations
490105 Dynamical systems in applications
Socio-Economic Objective (SEO) 2020: 280118 Expanding knowledge in the mathematical sciences
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
Appears in Collections:Journal Article
School of Science and Technology

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