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Local and Global Existence for Nonlocal Multispecies Advection-Diffusion Models

Valeria Giunta Orcid Logo, Thomas Hillen Orcid Logo, Mark Lewis, Jonathan R. Potts Orcid Logo

SIAM Journal on Applied Dynamical Systems, Volume: 21, Issue: 3, Pages: 1686 - 1708

Swansea University Author: Valeria Giunta Orcid Logo

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DOI (Published version): 10.1137/21m1425992

Abstract

Nonlocal advection is a key process in a range of biological systems, from cells within individuals to the movement of whole organisms. Consequently, in recent years, there has been increasing attention on modeling non-local advection mathematically. These often take the form of partial differential...

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Published in: SIAM Journal on Applied Dynamical Systems
ISSN: 1536-0040
Published: Society for Industrial and Applied Mathematics (SIAM) 2022
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URI: https://cronfa.swan.ac.uk/Record/cronfa64697
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first_indexed 2023-10-10T11:15:41Z
last_indexed 2023-10-10T11:15:41Z
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spelling v2 64697 2023-10-10 Local and Global Existence for Nonlocal Multispecies Advection-Diffusion Models 50456cce4b2c7be66f8302d418963b0c 0000-0003-1156-7136 Valeria Giunta Valeria Giunta true false 2023-10-10 SMA Nonlocal advection is a key process in a range of biological systems, from cells within individuals to the movement of whole organisms. Consequently, in recent years, there has been increasing attention on modeling non-local advection mathematically. These often take the form of partial differential equations, with integral terms modeling the nonlocality. One common formalism is the aggregation-diffusion equation, a class of advection-diffusion models with nonlocal advection. This was originally used to model a single population but has recently been extended to the multispecies case to model the way organisms may alter their movement in the presence of coexistent species. Here we prove existence theorems for a class of nonlocal multispecies advection-diffusion models, with an arbitrary number of coexistent species. We prove global existence for models in n = 1 spatial dimension and local existence for n > 1. We describe an efficient spectral method for numerically solving these models and provide an example simulation output. Overall, this helps provide a solid mathematical foundation for studying the effect of interspecies interactions on movement and space use. Journal Article SIAM Journal on Applied Dynamical Systems 21 3 1686 1708 Society for Industrial and Applied Mathematics (SIAM) 1536-0040 Advection-diffusion, aggregation-diffusion, existence theorems, mathematical ecology, nonlocal advection, taxis 30 9 2022 2022-09-30 10.1137/21m1425992 http://dx.doi.org/10.1137/21m1425992 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University VG and JRP acknowledge the support of an Engineering and Physical Sciences Research Council (EPSRC) grant EP/V002988/1 awarded to JRP. VG also acknowledges support from GNFM-INdAM and the Italian MIUR through project PRIN2017 2017YBKNCE. TH is grateful for support from the Natural Science and Engineering Council of Canada Discovery Grant RGPIN-2017-04158. MAL gratefully acknowledges support from the NSERC Discovery and Canada Research Chair programs. 2023-12-01T17:41:01.4945051 2023-10-10T12:13:47.3607711 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Valeria Giunta 0000-0003-1156-7136 1 Thomas Hillen 0000-0003-0819-9520 2 Mark Lewis 3 Jonathan R. Potts 0000-0002-8564-2904 4
title Local and Global Existence for Nonlocal Multispecies Advection-Diffusion Models
spellingShingle Local and Global Existence for Nonlocal Multispecies Advection-Diffusion Models
Valeria Giunta
title_short Local and Global Existence for Nonlocal Multispecies Advection-Diffusion Models
title_full Local and Global Existence for Nonlocal Multispecies Advection-Diffusion Models
title_fullStr Local and Global Existence for Nonlocal Multispecies Advection-Diffusion Models
title_full_unstemmed Local and Global Existence for Nonlocal Multispecies Advection-Diffusion Models
title_sort Local and Global Existence for Nonlocal Multispecies Advection-Diffusion Models
author_id_str_mv 50456cce4b2c7be66f8302d418963b0c
author_id_fullname_str_mv 50456cce4b2c7be66f8302d418963b0c_***_Valeria Giunta
author Valeria Giunta
author2 Valeria Giunta
Thomas Hillen
Mark Lewis
Jonathan R. Potts
format Journal article
container_title SIAM Journal on Applied Dynamical Systems
container_volume 21
container_issue 3
container_start_page 1686
publishDate 2022
institution Swansea University
issn 1536-0040
doi_str_mv 10.1137/21m1425992
publisher Society for Industrial and Applied Mathematics (SIAM)
college_str Faculty of Science and Engineering
hierarchytype
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
url http://dx.doi.org/10.1137/21m1425992
document_store_str 0
active_str 0
description Nonlocal advection is a key process in a range of biological systems, from cells within individuals to the movement of whole organisms. Consequently, in recent years, there has been increasing attention on modeling non-local advection mathematically. These often take the form of partial differential equations, with integral terms modeling the nonlocality. One common formalism is the aggregation-diffusion equation, a class of advection-diffusion models with nonlocal advection. This was originally used to model a single population but has recently been extended to the multispecies case to model the way organisms may alter their movement in the presence of coexistent species. Here we prove existence theorems for a class of nonlocal multispecies advection-diffusion models, with an arbitrary number of coexistent species. We prove global existence for models in n = 1 spatial dimension and local existence for n > 1. We describe an efficient spectral method for numerically solving these models and provide an example simulation output. Overall, this helps provide a solid mathematical foundation for studying the effect of interspecies interactions on movement and space use.
published_date 2022-09-30T17:41:02Z
_version_ 1784102217168453632
score 11.013148

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