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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2405.04666 |
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| _version_ | 1866929337582747648 |
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| author | Le, Minh |
| author_facet | Le, Minh |
| contents | We study the global existence and boundedness of solutions to a chemotaxis system with weakly singular sensitivity and sub-logistic sources in a two dimensional domain. X. Zhao (Nonlinearity; 2023; 36; 3909-3938 ) showed that the logistic degradation, $-μu^2$, can prevent blow-up under the largeness assumption on $μ$. In this paper, we improve the result by replacing the quadratic degradation by sub-logistic one, $-\frac{μu^2}{\ln^β(u+e)}$ with $β\in (0,1)$, and removing the largeness assumption on $μ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04666 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Boundedness in a chemotaxis system with weakly singular sensitivity in dimension two with arbitrary sub-quadratic degradation sources Le, Minh Analysis of PDEs We study the global existence and boundedness of solutions to a chemotaxis system with weakly singular sensitivity and sub-logistic sources in a two dimensional domain. X. Zhao (Nonlinearity; 2023; 36; 3909-3938 ) showed that the logistic degradation, $-μu^2$, can prevent blow-up under the largeness assumption on $μ$. In this paper, we improve the result by replacing the quadratic degradation by sub-logistic one, $-\frac{μu^2}{\ln^β(u+e)}$ with $β\in (0,1)$, and removing the largeness assumption on $μ$. |
| title | Boundedness in a chemotaxis system with weakly singular sensitivity in dimension two with arbitrary sub-quadratic degradation sources |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2405.04666 |