Finite-time blow-up in a quasilinear fully parabolic attraction-repulsion chemotaxis system with density-dependent sensitivity
This article concerns the quasilinear fully parabolic attraction-repulsion chemotaxis system $$\displaylines{ u_t=\nabla \cdot ((u+1)^{m-1}\nabla u -\chi u(u+1)^{p-2} \nabla v + \xi u(u+1)^{p-2}\nabla w),\quad x \in \Omega,\; t >0,\cr v_t=\Delta v+\alpha u-\beta v, \quad x \in \Omega,\; t >0,\...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2025-08-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2025/81/abstr.html |
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| _version_ | 1849341265727979520 |
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| author | Yutaro Chiyo Takeshi Uemura Tomomi Yokota |
| author_facet | Yutaro Chiyo Takeshi Uemura Tomomi Yokota |
| author_sort | Yutaro Chiyo |
| collection | DOAJ |
| description | This article concerns the quasilinear fully parabolic attraction-repulsion
chemotaxis system
$$\displaylines{
u_t=\nabla \cdot ((u+1)^{m-1}\nabla u -\chi u(u+1)^{p-2} \nabla v
+ \xi u(u+1)^{p-2}\nabla w),\quad x \in \Omega,\; t >0,\cr
v_t=\Delta v+\alpha u-\beta v, \quad x \in \Omega,\; t >0,\cr
w_t=\Delta w+\gamma u-\delta w, \quad x \in \Omega,\; t >0
}$$
with homogeneous Neumann boundary conditions,
where $\Omega \subset \mathbb{R}^n$ $(n \in \{2,3\})$ is an open ball,
$m, p \in \mathbb{R}$,
$\chi, \xi, \alpha, \beta, \gamma, \delta >0$ are constants.
The main result asserts finite-time blow-up of solutions to this system
with some positive initial data when $\chi\alpha-\xi\gamma >0$, $p \ge 2$ and
$p-m >2/n$. |
| format | Article |
| id | doaj-art-11806d109acc45e4841365d006c25aed |
| institution | Kabale University |
| issn | 1072-6691 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj-art-11806d109acc45e4841365d006c25aed2025-08-20T03:43:40ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912025-08-01202581,110Finite-time blow-up in a quasilinear fully parabolic attraction-repulsion chemotaxis system with density-dependent sensitivityYutaro Chiyo0Takeshi Uemura1Tomomi Yokota2 Tokyo Univ. of Science, Tokyo, Japan Tokyo Univ. of Science, Tokyo, Japan Tokyo Univ. of Science, Tokyo, Japan This article concerns the quasilinear fully parabolic attraction-repulsion chemotaxis system $$\displaylines{ u_t=\nabla \cdot ((u+1)^{m-1}\nabla u -\chi u(u+1)^{p-2} \nabla v + \xi u(u+1)^{p-2}\nabla w),\quad x \in \Omega,\; t >0,\cr v_t=\Delta v+\alpha u-\beta v, \quad x \in \Omega,\; t >0,\cr w_t=\Delta w+\gamma u-\delta w, \quad x \in \Omega,\; t >0 }$$ with homogeneous Neumann boundary conditions, where $\Omega \subset \mathbb{R}^n$ $(n \in \{2,3\})$ is an open ball, $m, p \in \mathbb{R}$, $\chi, \xi, \alpha, \beta, \gamma, \delta >0$ are constants. The main result asserts finite-time blow-up of solutions to this system with some positive initial data when $\chi\alpha-\xi\gamma >0$, $p \ge 2$ and $p-m >2/n$.http://ejde.math.txstate.edu/Volumes/2025/81/abstr.htmlfinite-time blow-upquasilinearattraction-repulsionchemotaxis |
| spellingShingle | Yutaro Chiyo Takeshi Uemura Tomomi Yokota Finite-time blow-up in a quasilinear fully parabolic attraction-repulsion chemotaxis system with density-dependent sensitivity Electronic Journal of Differential Equations finite-time blow-up quasilinear attraction-repulsion chemotaxis |
| title | Finite-time blow-up in a quasilinear fully parabolic attraction-repulsion chemotaxis system with density-dependent sensitivity |
| title_full | Finite-time blow-up in a quasilinear fully parabolic attraction-repulsion chemotaxis system with density-dependent sensitivity |
| title_fullStr | Finite-time blow-up in a quasilinear fully parabolic attraction-repulsion chemotaxis system with density-dependent sensitivity |
| title_full_unstemmed | Finite-time blow-up in a quasilinear fully parabolic attraction-repulsion chemotaxis system with density-dependent sensitivity |
| title_short | Finite-time blow-up in a quasilinear fully parabolic attraction-repulsion chemotaxis system with density-dependent sensitivity |
| title_sort | finite time blow up in a quasilinear fully parabolic attraction repulsion chemotaxis system with density dependent sensitivity |
| topic | finite-time blow-up quasilinear attraction-repulsion chemotaxis |
| url | http://ejde.math.txstate.edu/Volumes/2025/81/abstr.html |
| work_keys_str_mv | AT yutarochiyo finitetimeblowupinaquasilinearfullyparabolicattractionrepulsionchemotaxissystemwithdensitydependentsensitivity AT takeshiuemura finitetimeblowupinaquasilinearfullyparabolicattractionrepulsionchemotaxissystemwithdensitydependentsensitivity AT tomomiyokota finitetimeblowupinaquasilinearfullyparabolicattractionrepulsionchemotaxissystemwithdensitydependentsensitivity |