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 $$\displaylines{ u_t=\nabla \cdot ((u+1)^{m-1}\nabla u -\chi u(u+1)^{p-2} \nabla v + \xi u(u+1)^{p-2}\nabla w),\quad x \in \Omega,\; t >0,\cr v_t=\Delta v+\alpha u-\beta v, \quad x \in \Omega,\; t >0,\...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2025-08-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2025/81/abstr.html |
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| Summary: | This article concerns the quasilinear fully parabolic attraction-repulsion
chemotaxis system
$$\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
$p-m >2/n$. |
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| ISSN: | 1072-6691 |