Article
| Title: | Global solvability in the parabolic-elliptic chemotaxis system with singular sensitivity and logistic source (English) |
| Author: | Zhao, Xiangdong |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 1 |
| Year: | 2024 |
| Pages: | 127-151 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We study the chemotaxis system with singular sensitivity and logistic-type source: $u_t=\Delta u-\chi \nabla \cdot (u \nabla v/ v) +ru-\mu u^k$, $0=\Delta v-v+u$ under the non-flux boundary conditions in a smooth bounded domain $\Omega \subset \mathbb {R}^n$, $\chi ,r,\mu >0$, $k>1$ and $n\ge 1$. It is shown with $k\in (1,2)$ that the system possesses a global generalized solution for $n\ge 2$ which is bounded when $\chi >0$ is suitably small related to $r>0$ and the initial datum is properly small, and a global bounded classical solution for $n=1$. (English) |
| Keyword: | chemotaxis |
| Keyword: | singular sensitivity |
| Keyword: | global solvability |
| MSC: | 35B45 |
| MSC: | 35K55 |
| MSC: | 92C17 |
| DOI: | 10.21136/CMJ.2023.0544-22 |
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| Date available: | 2024-03-13T10:05:41Z |
| Last updated: | 2024-03-18 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152272 |
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