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Non-local effects on travelling waves arising in a moving-boundary reaction-diffusion model

Fadai, Nabil T.; Billingham, John

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Authors

NABIL FADAI NABIL.FADAI@NOTTINGHAM.AC.UK
Assistant Professor

JOHN BILLINGHAM john.billingham@nottingham.ac.uk
Professor of Theoretical Mechanics



Abstract

We examine travelling wave solutions of the partial differential equation u_t = u_xx + u(1 − u * φ) on a moving domain x ≤ L(t), where u * φ is the spatial convolution of the population density with a kernel φ(y). We provide asymptotic approximations of the resulting travelling waves in various asymptotic limits of the wavespeed, the non-local interaction strength, and the moving boundary condition. Crucially, we find that when the moving boundary has a weak interactive strength with the population density flux, there can be two different travelling wave solutions that move at the same wavespeed.

Journal Article Type Article
Acceptance Date Aug 31, 2022
Online Publication Date Sep 19, 2022
Publication Date Oct 7, 2022
Deposit Date Sep 1, 2022
Publicly Available Date Sep 20, 2023
Journal Journal of Physics A: Mathematical and Theoretical
Print ISSN 1751-8113
Electronic ISSN 1751-8121
Peer Reviewed Peer Reviewed
Volume 55
Issue 40
Article Number 405701
DOI https://doi.org/10.1088/1751-8121/ac8ef5
Keywords Fisher's equation; non-local differential equation; Stefan condition; moving boundary problem AMS classification scheme numbers: 35B40; 35C07; 35K57; 34B15; 41A60
Public URL https://nottingham-repository.worktribe.com/output/10634853
Publisher URL https://iopscience.iop.org/article/10.1088/1751-8121/ac8ef5

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