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arXiv · 2307.01011

On a chemotaxis model with nonlinear diffusion modelling multiple sclerosis

S. Fagioli·E. Radici·L. Romagnoli
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Abstract

We investigated existence of global weak solutions for a system of chemotaxis type with nonlinear degenerate diffusion, arising in modelling Multiple Sclerosis disease. The model consists of three equations describing the evolution of macrophages ($m$), cytokine ($c$) and apoptotic oligodendrocytes ($d$). The main novelty in our work is the presence of a nonlinear diffusivity $D(m)$, which results to be more appropriate from the modelling point of view. Under suitable assumptions and for sufficiently regular initial data, adapting the strategy in [30,44], we show the existence of global bounded solutions for the model analysed.

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S. Fagioli, E. Radici, L. Romagnoli. 2023-07-03. On a chemotaxis model with nonlinear diffusion modelling multiple sclerosis. https://arxiv.org/abs/2307.01011

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