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

Published online by Cambridge University Press:  28 July 2021

Laurent Desvillettes
Affiliation:
Université de Paris, Sorbonne Université, CNRS Institut de Mathématiques de Jussieu-Paris Rive Gauche, Paris, France ([email protected])
Valeria Giunta
Affiliation:
Department of Engineering, University of Palermo, Palermo, Italy ([email protected])
Jeff Morgan
Affiliation:
Department of Mathematics, University of Houston, Houston, Texas 77004, USA ([email protected])
Bao Quoc Tang
Affiliation:
Institute of Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, 8010 Graz, Austria ([email protected], [email protected])

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 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.

Type
Research Article
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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