2023/07/03 by Simone Fagioli, Fagioli, S., Emanuela Radici +3
Immunology and Microbiology · Mathematics · Medicine · #35B45 #35K57 #35K65 #35Q92 #92C17 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Reproductive System and Pregnancy
paper · pdf · doi:10.48550/arxiv.2307.01011
openalex publication_date 2023/07/03 · openalex created_date 2023/07/05 · openalex updated_date 2026/08/01
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.