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Reaction–Diffusion Problems on Time-Periodic Domains

Jane Allwright

Journal of Dynamics and Differential Equations

Swansea University Author: Jane Allwright

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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...

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Published in: Journal of Dynamics and Differential Equations
ISSN: 1040-7294 1572-9222
Published: Springer Science and Business Media LLC 2023
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URI: https://cronfa.swan.ac.uk/Record/cronfa64113
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first_indexed 2023-09-11T08:56:11Z
last_indexed 2023-09-11T08:56:11Z
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spelling v2 64113 2023-08-23 Reaction–Diffusion Problems on Time-Periodic Domains cb793783c92e676896135595f2f736f1 Jane Allwright Jane Allwright true false 2023-08-23 MACS 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. Journal Article Journal of Dynamics and Differential Equations Springer Science and Business Media LLC 1040-7294 1572-9222 Time-periodic domain · Principal periodic eigenvalue · Reaction–diffusion 23 9 2023 2023-09-23 10.1007/s10884-023-10308-9 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University SU Library paid the OA fee (TA Institutional Deal) The author is grateful for an EPSRC-funded studentship: EPSRC DTP grant EP/R51312X/1, and research associate funding: EP/W522545/1. 2024-09-16T16:34:32.0115089 2023-08-23T14:54:41.9257009 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Jane Allwright 1 64113__28674__f1db2e430ff84452bbf9e73aa1e8f64b.pdf 64113.VOR.pdf 2023-10-02T12:07:37.6234011 Output 461550 application/pdf Version of Record true 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. true eng http://creativecommons.org/licenses/by/4.0/
title Reaction–Diffusion Problems on Time-Periodic Domains
spellingShingle Reaction–Diffusion Problems on Time-Periodic Domains
Jane Allwright
title_short Reaction–Diffusion Problems on Time-Periodic Domains
title_full Reaction–Diffusion Problems on Time-Periodic Domains
title_fullStr Reaction–Diffusion Problems on Time-Periodic Domains
title_full_unstemmed Reaction–Diffusion Problems on Time-Periodic Domains
title_sort Reaction–Diffusion Problems on Time-Periodic Domains
author_id_str_mv cb793783c92e676896135595f2f736f1
author_id_fullname_str_mv cb793783c92e676896135595f2f736f1_***_Jane Allwright
author Jane Allwright
author2 Jane Allwright
format Journal article
container_title Journal of Dynamics and Differential Equations
publishDate 2023
institution Swansea University
issn 1040-7294
1572-9222
doi_str_mv 10.1007/s10884-023-10308-9
publisher Springer Science and Business Media LLC
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
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description 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.
published_date 2023-09-23T16:34:30Z
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score 11.036706

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