Existence of Weak Solutions to a Constrained Aggregation-Diffusion-Reaction Model for Multiple Sclerosis
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910002067800064 |
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| author | Fagioli, S. Katapady, M. Kamath |
| author_facet | Fagioli, S. Katapady, M. Kamath |
| contents | We establish an existence result for weak solutions to an aggregation-diffusion-reaction equation with a constraint, arising in the modelling of multiple sclerosis. The model is derived from a general chemotaxis-type framework and describes the time evolution of the density of activated macrophages, which is subject to attraction by oligodendrocytes. The latter are governed by a constraint equation. The proof relies on a variational splitting scheme that isolates the transport (aggregation-diffusion) and reaction contributions. The structure of the constraint makes it possible to recover the oligodendrocyte density as the limit of a sequence of characteristic functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19427 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Existence of Weak Solutions to a Constrained Aggregation-Diffusion-Reaction Model for Multiple Sclerosis Fagioli, S. Katapady, M. Kamath Analysis of PDEs 35K65, 35Q92, 35A15, 45K05, 92C17 We establish an existence result for weak solutions to an aggregation-diffusion-reaction equation with a constraint, arising in the modelling of multiple sclerosis. The model is derived from a general chemotaxis-type framework and describes the time evolution of the density of activated macrophages, which is subject to attraction by oligodendrocytes. The latter are governed by a constraint equation. The proof relies on a variational splitting scheme that isolates the transport (aggregation-diffusion) and reaction contributions. The structure of the constraint makes it possible to recover the oligodendrocyte density as the limit of a sequence of characteristic functions. |
| title | Existence of Weak Solutions to a Constrained Aggregation-Diffusion-Reaction Model for Multiple Sclerosis |
| topic | Analysis of PDEs 35K65, 35Q92, 35A15, 45K05, 92C17 |
| url | https://arxiv.org/abs/2601.19427 |