Critical mass phenomena in higher dimensional quasilinear Keller–Segel systems with indirect signal production

Abstract

In this paper, we deal with quasilinear Keller–Segel systems with indirect signal production, complemented with homogeneous Neumann boundary conditions and suitable initial conditions, where is a bounded smooth domain, and We show that in the case , there exists such that if either or , then the solution exists globally and remains bounded, and that in the case , if either or , then there exist radially symmetric initial data such that and the solution blows up in finite or infinite time, where the blow‐up time is infinite if . In particular, if , there is a critical mass phenomenon in the sense that is a finite positive number.