Yutaro Chiyo, Takeshi Uemura, Tomomi Yokota
Abstract:
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
\(p-m >2/n\).
Submitted May 1, 2025. Published August 6, 2025.
Math Subject Classifications: 35B44, 35K59, 35Q92, 92C17.
Key Words: Finite-time blow-up; quasilinear; attraction-repulsion; chemotaxis.
DOI: 10.58997/ejde.2025.81
Show me the PDF file (387 KB), TEX file for this article.
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Yutaro Chiyo Department of Mathematics Tokyo University of Science 1-3, Kagurazaka, Shinjuku-ku Tokyo 162-8601, Japan email: ycnewssz@gmail.com |
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Takeshi Uemura Department of Mathematics Tokyo University of Science 1-3, Kagurazaka, Shinjuku-ku Tokyo 162-8601, Japan email: uemura.tus@gmail.com} |
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Tomomi Yokota Department of Mathematics Tokyo University of Science 1-3, Kagurazaka, Shinjuku-ku Tokyo 162-8601, Japan email: yokota@rs.tus.ac.jp |
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