Finite-time blow-up in a quasilinear fully parabolic attraction-repulsion chemotaxis system with density-dependent sensitivity

• Published in: Electronic journal of differential equations Vol. 2025; no. 1-??; pp. 1 - 10
• Main Authors: Chiyo, Yutaro, Uemura, Takeshi, Yokota, Tomomi
• Format: Journal Article
• Language: English
• Published: Texas State University 06.08.2025
• Subjects: attraction-repulsion; chemotaxis; finite-time blow-up; quasilinear
• ISSN: 1072-6691; 1072-6691
• DOI: 10.58997/ejde.2025.81

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 \(p-m>2/n\). For more information see https://ejde.math.txstate.edu/Volumes/2025/81/abstr.html