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Local and Global Existence for Nonlocal Multispecies Advection-Diffusion Models
,
Thomas Hillen ,
Mark Lewis,
Jonathan R. Potts
SIAM Journal on Applied Dynamical Systems, Volume: 21, Issue: 3, Pages: 1686 - 1708
Swansea University Author:
Valeria Giunta
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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...
| Published in: | SIAM Journal on Applied Dynamical Systems |
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| ISSN: | 1536-0040 |
| Published: |
Society for Industrial and Applied Mathematics (SIAM)
2022
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| Online Access: |
Check full text
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa64697 |
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| 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 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. |
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| Keywords: |
Advection-diffusion, aggregation-diffusion, existence theorems, mathematical ecology, nonlocal advection, taxis |
| College: |
Faculty of Science and Engineering |
| Funders: |
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. |
| Issue: |
3 |
| Start Page: |
1686 |
| End Page: |
1708 |