Please use this identifier to cite or link to this item: https://hdl.handle.net/1959.11/56291
Title: A delay induced nonlocal free boundary problem
Contributor(s): Du, Yihong  (author)orcid ; Fang, Jian (author); Sun, Ningkui (author)
Publication Date: 2023-08
Early Online Version: 2022-08-08
Open Access: Yes
DOI: 10.1007/s00208-022-02451-3
Handle Link: https://hdl.handle.net/1959.11/56291
Abstract: 

We study the dynamics of a population with an age structure whose population range expands with time, where the adult population is assumed to satisfy a reaction– diffusion equation over a changing interval determined by a Stefan type free boundary condition, while the juvenile population satisfies a reaction–diffusion equation whose evolving domain is determined by the adult population. The interactions between the adult and juvenile populations involve a fixed time-delay, which renders the model nonlocal in nature. After establishing the well-posedness of the model, we obtain a rather complete description of its long-time dynamical behaviour, which is shown to follow a spreading–vanishing dichotomy. When spreading persists, we show that the population range expands with an asymptotic speed, which is uniquely determined by an associated nonlocal elliptic problem over the half line. We hope this work will inspire further research on age-structured population models with an evolving population range.

Publication Type: Journal Article
Grant Details: ARC/DP220101820
Source of Publication: Mathematische Annalen, 386(3-4), p. 2061-2106
Publisher: Springer
Place of Publication: Germany
ISSN: 1432-1807
0025-5831
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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