Blow-up of nonradial solutions to the hyperbolic-elliptic chemotaxis system with logistic source
This paper is concerned with the blow-up of solutions to the following hyperbolic-elliptic chemotaxis system: \begin{equation*} {\left\lbrace \begin{array}{ll} u_{t} =-\nabla \cdot (\chi u \nabla v)+g(u), \qquad x\in \Omega , \ t>0,\\ \;\;\; 0 =\Delta v-v+u, \hspace{58.33328pt}x\in \Omega , \ t&...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2023-01-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.397/ |
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| Summary: | This paper is concerned with the blow-up of solutions to the following hyperbolic-elliptic chemotaxis system:
\begin{equation*}
{\left\lbrace \begin{array}{ll} u_{t} =-\nabla \cdot (\chi u \nabla v)+g(u), \qquad x\in \Omega , \ t>0,\\ \;\;\; 0 =\Delta v-v+u, \hspace{58.33328pt}x\in \Omega , \ t>0, \end{array}\right.}
\end{equation*}
under homogeneous Neumann boundary conditions in a bounded domain $ \Omega \subset \mathbb{R}^{n}, n\ge 1,$ with smooth boundary and the function $g$ is assumed to generalize the logistic source:
\begin{equation*}
g(s)\le a s - b s^{\gamma }\ \text{ for} \ s>0
\end{equation*}
with $1<\gamma \le 2.$ For $b<\chi $ and some suitable conditions on parameters of problem, we prove that the solutions of this problem blow up in finite time. This result extend the obtained results for this problem. |
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| ISSN: | 1778-3569 |