Global Boundedness and Finite-Time Blow-up for a Quasilinear Chemotaxis--May--Nowak System

Abstract

This paper continues the work of Bai, Li, Liu and Luo \cite{BaiLiLiuLuoPreprint} on a quasilinear chemotaxis--May--Nowak system. We establish global boundedness in three dimensions for both the parabolic--elliptic--parabolic and fully parabolic systems when $m>4/3$. For the former, we construct finite-time blow-up solutions in balls when $n=3$ and $1<m\le 4/3$, and when $n\ge 4$ and $0<m\le 2-2/n$.