Remarks on finite-time blow-up in a fully parabolic attraction-repulsion chemotaxis system via reduction to the Keller-Segel system

Yutaro Chiyo, Tomomi Yokota

Published 2021-03-03Version 1

This paper deals with the fully parabolic attraction-repulsion chemotaxis system, \begin{align*} u_t=\Delta u-\chi\nabla \cdot (u\nabla v)+\xi \nabla\cdot(u \nabla w), \quad v_t=\Delta v-v+u, \quad w_t=\Delta w-w+u, \quad x \in \Omega,\ t>0 \end{align*} under homogeneous Neumann boundary conditions and initial conditions, where $\Omega$ is an open ball in $\mathbb{R}^n$ ($n \ge 3$), $\chi, \xi>0$ are constants. When $w=0$, finite-time blow-up in the corresponding Keller-Segel system has already been obtained. However, finite-time blow-up in the above attraction-repulsion chemotaxis system has not yet been established. This paper provides an answer to this open problem by using a transformation with the structural advantage of the system.