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Global well-posedness and nonlinear stability of a chemotaxis system modelling multiple sclerosis

Laurent Desvillettes, Valeria Giunta Orcid Logo, Jeff Morgan, Bao Quoc Tang

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume: 152, Issue: 4, Pages: 826 - 856

Swansea University Author: Valeria Giunta Orcid Logo

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DOI (Published version): 10.1017/prm.2021.33

Abstract

We consider a system of reaction–diffusion equations including chemotaxis terms and coming out of the modelling of multiple sclerosis. The global existence of strong solutions to this system in any dimension is proved, and it is also shown that the solution is bounded uniformly in time. Finally, a n...

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Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics
ISSN: 0308-2105 1473-7124
Published: Cambridge University Press (CUP) 2022
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URI: https://cronfa.swan.ac.uk/Record/cronfa64700
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first_indexed 2023-10-10T11:20:42Z
last_indexed 2023-10-10T11:20:42Z
id cronfa64700
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spelling v2 64700 2023-10-10 Global well-posedness and nonlinear stability of a chemotaxis system modelling multiple sclerosis 50456cce4b2c7be66f8302d418963b0c 0000-0003-1156-7136 Valeria Giunta Valeria Giunta true false 2023-10-10 SMA We consider a system of reaction–diffusion equations including chemotaxis terms and coming out of the modelling of multiple sclerosis. The global existence of strong solutions to this system in any dimension is proved, and it is also shown that the solution is bounded uniformly in time. Finally, a nonlinear stability result is obtained when the chemotaxis term is not too big. We also perform numerical simulations to show the appearance of Turing patterns when the chemotaxis term is large. Journal Article Proceedings of the Royal Society of Edinburgh: Section A Mathematics 152 4 826 856 Cambridge University Press (CUP) 0308-2105 1473-7124 Chemotaxis models, Global solutions, Uniform-in-time bounds, Nonlinear stability, Cross diffusion 31 8 2022 2022-08-31 10.1017/prm.2021.33 http://dx.doi.org/10.1017/prm.2021.33 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2023-11-28T14:30:12.1639763 2023-10-10T12:19:14.4814839 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Laurent Desvillettes 1 Valeria Giunta 0000-0003-1156-7136 2 Jeff Morgan 3 Bao Quoc Tang 4
title Global well-posedness and nonlinear stability of a chemotaxis system modelling multiple sclerosis
spellingShingle Global well-posedness and nonlinear stability of a chemotaxis system modelling multiple sclerosis
Valeria Giunta
title_short Global well-posedness and nonlinear stability of a chemotaxis system modelling multiple sclerosis
title_full Global well-posedness and nonlinear stability of a chemotaxis system modelling multiple sclerosis
title_fullStr Global well-posedness and nonlinear stability of a chemotaxis system modelling multiple sclerosis
title_full_unstemmed Global well-posedness and nonlinear stability of a chemotaxis system modelling multiple sclerosis
title_sort Global well-posedness and nonlinear stability of a chemotaxis system modelling multiple sclerosis
author_id_str_mv 50456cce4b2c7be66f8302d418963b0c
author_id_fullname_str_mv 50456cce4b2c7be66f8302d418963b0c_***_Valeria Giunta
author Valeria Giunta
author2 Laurent Desvillettes
Valeria Giunta
Jeff Morgan
Bao Quoc Tang
format Journal article
container_title Proceedings of the Royal Society of Edinburgh: Section A Mathematics
container_volume 152
container_issue 4
container_start_page 826
publishDate 2022
institution Swansea University
issn 0308-2105
1473-7124
doi_str_mv 10.1017/prm.2021.33
publisher Cambridge University Press (CUP)
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/10.1017/prm.2021.33
document_store_str 0
active_str 0
description We consider a system of reaction–diffusion equations including chemotaxis terms and coming out of the modelling of multiple sclerosis. The global existence of strong solutions to this system in any dimension is proved, and it is also shown that the solution is bounded uniformly in time. Finally, a nonlinear stability result is obtained when the chemotaxis term is not too big. We also perform numerical simulations to show the appearance of Turing patterns when the chemotaxis term is large.
published_date 2022-08-31T14:30:13Z
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score 11.013148

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