Prevention of Infinite-time Blowup by Slightly Super-linear Degradation in a Keller--Segel System with Density-suppressed Motility
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910290986139648 |
|---|---|
| author | Xiao, Yamin Jiang, Jie |
| author_facet | Xiao, Yamin Jiang, Jie |
| contents | An initial-Neumann boundary value problem for a Keller--Segel system with density-suppressed motility and source terms is considered. Infinite-time blowup of the classical solution was previously observed for its source-free version when dimension $N\geq2$. In this work, we prove that with any source term involving a slightly super-linear degradation effect on the density, of a growth order of $s\log s$ at most, the classical solution is uniformly-in-time bounded when $N\leq3$, thus preventing the infinite-time explosion detected in the source-free counter-part. The cornerstone of our proof lies in an improved comparison argument and a construction of an entropy inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04424 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Prevention of Infinite-time Blowup by Slightly Super-linear Degradation in a Keller--Segel System with Density-suppressed Motility Xiao, Yamin Jiang, Jie Analysis of PDEs An initial-Neumann boundary value problem for a Keller--Segel system with density-suppressed motility and source terms is considered. Infinite-time blowup of the classical solution was previously observed for its source-free version when dimension $N\geq2$. In this work, we prove that with any source term involving a slightly super-linear degradation effect on the density, of a growth order of $s\log s$ at most, the classical solution is uniformly-in-time bounded when $N\leq3$, thus preventing the infinite-time explosion detected in the source-free counter-part. The cornerstone of our proof lies in an improved comparison argument and a construction of an entropy inequality. |
| title | Prevention of Infinite-time Blowup by Slightly Super-linear Degradation in a Keller--Segel System with Density-suppressed Motility |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.04424 |