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This paper deals with finite-time blow-up of solutions to the quasilinear degenerate parabolic–elliptic chemotaxis system with logistic source and nonlinear production,\begin{document}$ \begin{align*} \begin{cases}u_t = \Delta u^m - \chi \nabla \cdot (u^\alpha \nabla v)+ \lambda u - \mu u^\kappa, \quad &amp;amp;x \in \Omega, \ t&amp;gt;0, \\0 = \Delta v - \overline{M_\ell}(t) + u^\ell, \quad &amp;amp;x \in \Omega, \ t&amp;gt;0, \end{cases} \end{align*} $\end{document}where   \begin{document}$ \Omega: = B_R(0) \subset \mathbb{R}^n \ (n \in \mathbb{N}) $\end{document}   be a ball with some   \begin{document}$ R&amp;gt;0 $\end{document}   and   \begin{document}$ m\ge1 $\end{document}  ,   \begin{document}$ \chi&amp;gt;0 $\end{document}  ,   \begin{document}$ \alpha\ge1 $\end{document}  ,   \begin{document}$ \lambda&amp;gt;0 $\end{document}  ,   \begin{document}$ \mu&amp;gt;0 $\end{document}  ,   \begin{document}$ \kappa&amp;gt;1 $\end{document}  ,   \begin{document}$ \ell&amp;gt;0 $\end{document}   as well as   \begin{document}$ \overline{M_\ell}(t) $\end{document}   is the average of   \begin{document}$ u^\ell $\end{document}   over   \begin{document}$ \Omega $\end{document}  . As to the corresponding system with nondegenerate diffusion, finite-time blow-up has been obtained under the condition that   \begin{document}$ \alpha-\ell&amp;gt;\max\left\{\overline{m} +\frac{2}{n}\kappa, \kappa\right\} $\end{document}  , where   \begin{document}$ \overline{m}: = \max\{m,0\} $\end{document}   in a previous paper [ 26 ], which is based a work by Fuest [ 7 ]. The purpose of this paper is to establish finite-time blow-up for the above degenerate chemotaxis system within a concept of weak solutions with a moment inequality leading to blow-up.

Finite-time blow-up in a quasilinear degenerate parabolic–elliptic chemotaxis system with logistic source and nonlinear production