On a chemotaxis model with nonlinear diffusion modelling multiple sclerosis
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916239636430848 |
|---|---|
| author | Fagioli, S. Radici, E. Romagnoli, L. |
| author_facet | Fagioli, S. Radici, E. Romagnoli, L. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_01011 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On a chemotaxis model with nonlinear diffusion modelling multiple sclerosis Fagioli, S. Radici, E. Romagnoli, L. Analysis of PDEs 35K65, 35B45, 35Q92, 35K57, 92C17 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. |
| title | On a chemotaxis model with nonlinear diffusion modelling multiple sclerosis |
| topic | Analysis of PDEs 35K65, 35B45, 35Q92, 35K57, 92C17 |
| url | https://arxiv.org/abs/2307.01011 |