Generalized Doubly Parabolic Keller-Segel System with Fractional Diffusion
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866908284742533120 |
|---|---|
| author | Bronzi, Anne Caroline de Andrade, Crystianne Lilian |
| author_facet | Bronzi, Anne Caroline de Andrade, Crystianne Lilian |
| contents | The Keller-Segel model is a system of partial differential equations that describes the movement of cells or organisms in response to chemical signals, a phenomenon known as chemotaxis. In this study, we analyze a doubly parabolic Keller-Segel system in the whole space $\mathbb{R}^d$, $d\geq 2$, where both cellular and chemical diffusion are governed by fractional Laplacians with distinct exponents. This system generalizes the classical Keller-Segel model by introducing superdiffusion, a form of anomalous diffusion. This extension accounts for nonlocal diffusive effects observed in experimental settings, particularly in environments with sparse targets. We establish results on the local well-posedness of mild solutions for this generalized system and global well-posedness under smallness assumptions on the initial conditions in $L^p(\mathbb{R}^d)$. Furthermore, we characterize the asymptotic behavior of the solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09871 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Doubly Parabolic Keller-Segel System with Fractional Diffusion Bronzi, Anne Caroline de Andrade, Crystianne Lilian Analysis of PDEs 35Q92, 92C17, 35K55, 92B99 The Keller-Segel model is a system of partial differential equations that describes the movement of cells or organisms in response to chemical signals, a phenomenon known as chemotaxis. In this study, we analyze a doubly parabolic Keller-Segel system in the whole space $\mathbb{R}^d$, $d\geq 2$, where both cellular and chemical diffusion are governed by fractional Laplacians with distinct exponents. This system generalizes the classical Keller-Segel model by introducing superdiffusion, a form of anomalous diffusion. This extension accounts for nonlocal diffusive effects observed in experimental settings, particularly in environments with sparse targets. We establish results on the local well-posedness of mild solutions for this generalized system and global well-posedness under smallness assumptions on the initial conditions in $L^p(\mathbb{R}^d)$. Furthermore, we characterize the asymptotic behavior of the solution. |
| title | Generalized Doubly Parabolic Keller-Segel System with Fractional Diffusion |
| topic | Analysis of PDEs 35Q92, 92C17, 35K55, 92B99 |
| url | https://arxiv.org/abs/2501.09871 |