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

Fadai, Nabil T.; Billingham, John

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.

Citation

Fadai, N. T., & Billingham, J. (2022). Non-local effects on travelling waves arising in a moving-boundary reaction-diffusion model. Journal of Physics A: Mathematical and Theoretical, 55(40), Article 405701. https://doi.org/10.1088/1751-8121/ac8ef5

• 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