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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| Format: | Article |
| Language: | English |
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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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| author | Baghaei, khadijeh |
| author_facet | Baghaei, khadijeh |
| author_sort | Baghaei, khadijeh |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a5fe3be03d684bfba0499d4313240f38 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-a5fe3be03d684bfba0499d4313240f382025-02-07T11:06:07ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-01-01361G120721510.5802/crmath.39710.5802/crmath.397Blow-up of nonradial solutions to the hyperbolic-elliptic chemotaxis system with logistic sourceBaghaei, khadijeh0School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, IranThis 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.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.397/ |
| spellingShingle | Baghaei, khadijeh Blow-up of nonradial solutions to the hyperbolic-elliptic chemotaxis system with logistic source Comptes Rendus. Mathématique |
| title | Blow-up of nonradial solutions to the hyperbolic-elliptic chemotaxis system with logistic source |
| title_full | Blow-up of nonradial solutions to the hyperbolic-elliptic chemotaxis system with logistic source |
| title_fullStr | Blow-up of nonradial solutions to the hyperbolic-elliptic chemotaxis system with logistic source |
| title_full_unstemmed | Blow-up of nonradial solutions to the hyperbolic-elliptic chemotaxis system with logistic source |
| title_short | Blow-up of nonradial solutions to the hyperbolic-elliptic chemotaxis system with logistic source |
| title_sort | blow up of nonradial solutions to the hyperbolic elliptic chemotaxis system with logistic source |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.397/ |
| work_keys_str_mv | AT baghaeikhadijeh blowupofnonradialsolutionstothehyperbolicellipticchemotaxissystemwithlogisticsource |