No Cover Image

Journal article 334 views 28 downloads

Reaction–Diffusion Problems on Time-Periodic Domains

Jane Allwright

Journal of Dynamics and Differential Equations

Swansea University Author: Jane Allwright

  • 64113.VOR.pdf

    PDF | Version of Record

    This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

    Download (450.73KB)

Check full text

DOI (Published version): 10.1007/s10884-023-10308-9

Abstract

Reaction-diffusion equations are studied on bounded, time-periodic domains with zero Dirichlet boundary conditions. The long-time behaviour is shown to depend on the principal periodic eigenvalue of a transformed periodic-parabolic problem. We prove upper and lower bounds on this eigenvalue under a...

Full description

Published in: Journal of Dynamics and Differential Equations
ISSN: 1040-7294 1572-9222
Published: Springer Science and Business Media LLC 2023
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa64113
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract: Reaction-diffusion equations are studied on bounded, time-periodic domains with zero Dirichlet boundary conditions. The long-time behaviour is shown to depend on the principal periodic eigenvalue of a transformed periodic-parabolic problem. We prove upper and lower bounds on this eigenvalue under a range of different assumptions on the domain, and apply them to examples. The principal eigenvalue is considered as a function of the frequency, and results are given regarding its behaviour in the small and large frequency limits. A monotonicity property with respect to frequency is also proven. A reaction-diffusion problem with a class of monostable nonlinearity is then studied on a periodic domain, and we prove convergence to either zero or a unique positive periodic solution.
Keywords: Time-periodic domain · Principal periodic eigenvalue · Reaction–diffusion
College: Faculty of Science and Engineering
Funders: The author is grateful for an EPSRC-funded studentship: EPSRC DTP grant EP/R51312X/1, and research associate funding: EP/W522545/1.

Similar Items