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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2401.17697 |
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| _version_ | 1866913216771129344 |
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| author | Lu, Aijing Jiang, Jie |
| author_facet | Lu, Aijing Jiang, Jie |
| contents | In this paper, we consider an initial-Neumann boundary value problem for a parabolic-elliptic Keller-Segel system with signal-dependent motility and a source term. Previous research has rigorously shown that the source-free version of this system exhibits an infinite-time blowup phenomenon when dimension $N \geq 2$. In the current work, when $N \leq 3$, we establish uniform boundedness of global classical solutions with an additional source term that involves slightly super-linear degradation effect on the density, of a maximum growth order $s\log s$, unveiling a sufficient blowup suppression mechanism. The motility function considered in our work takes a rather general form compared with recent works \cite{FuJi2020, LyWa2023} which were restricted to the monotone non-increasing case. The cornerstone of our proof lies in deriving an upper bound for the second component of the system and an entropy-like estimate, which are achieved through tricky comparison skills and energy methods, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17697 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Suppression of Blowup by Slightly Superlinear Degradation in a Parabolic-Elliptic Keller--Segel System with Signal-dependent Motility Lu, Aijing Jiang, Jie Analysis of PDEs In this paper, we consider an initial-Neumann boundary value problem for a parabolic-elliptic Keller-Segel system with signal-dependent motility and a source term. Previous research has rigorously shown that the source-free version of this system exhibits an infinite-time blowup phenomenon when dimension $N \geq 2$. In the current work, when $N \leq 3$, we establish uniform boundedness of global classical solutions with an additional source term that involves slightly super-linear degradation effect on the density, of a maximum growth order $s\log s$, unveiling a sufficient blowup suppression mechanism. The motility function considered in our work takes a rather general form compared with recent works \cite{FuJi2020, LyWa2023} which were restricted to the monotone non-increasing case. The cornerstone of our proof lies in deriving an upper bound for the second component of the system and an entropy-like estimate, which are achieved through tricky comparison skills and energy methods, respectively. |
| title | Suppression of Blowup by Slightly Superlinear Degradation in a Parabolic-Elliptic Keller--Segel System with Signal-dependent Motility |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.17697 |