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

2020/09/28 by Laurent Desvillettes, Valeria Giunta, Desvillettes, Laurent +5
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.2009.13131

3 figures

arxiv created 2020/09/28 · arxiv updated 2020/09/29

Abstract

We consider a system of reaction-diffusion equations including chemotaxis terms and coming out of the modeling 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.

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