| 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. We first show the existence of global bounded solutions for the model. We then investigate some properties on the stationary states and pattern formation. |
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