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Existence and regularity for a chemotaxis model involved in the modeling of multiple sclerosis

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Abstract

We study in this work the global existence of solutions to a system of reaction cross diffusion equations appearing in the modeling of multiple sclerosis, in the one-dimensional case. Weak solutions are obtained for general initial data, and existence, uniqueness, stability and smoothness are proven when initial data are smooth.

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Acknowledgements

This paper is dedicated to Professor M. Sugiyama and Professor G. Toscani at the occasion of their seventieth birthday.

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Authors and Affiliations

  1. Institut de Mathématiques de Jussieu-Paris Rive Gauche, Université de Paris, Sorbonne Université, CNRS, 75013, Paris, France

    Laurent Desvillettes

  2. Department of Mathematics and Computer Science, University of Palermo, Via Archirafi, 34, 90127, Palermo, Italy

    Valeria Giunta

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  1. Laurent Desvillettes
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  2. Valeria Giunta
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Correspondence to Laurent Desvillettes.

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Desvillettes, L., Giunta, V. Existence and regularity for a chemotaxis model involved in the modeling of multiple sclerosis. Ricerche mat 70, 99–113 (2021). https://doi.org/10.1007/s11587-020-00495-8

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  • DOI: https://doi.org/10.1007/s11587-020-00495-8

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