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chemotaxis models

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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Global well-posedness and nonlinear stability of a chemotaxis system modelling multiple sclerosis
Part of
Laurent Desvillettes, Valeria Giunta, Jeff Morgan, Bao Quoc Tang
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 152 / Issue 4 / August 2022

Published online by Cambridge University Press:

28 July 2021, pp. 826-856

Print publication:

August 2022
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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.