Blow-up of a higher-dimensional Keller-Segel system with logistic source

Abstract:

The Cauchy problem of the Keller-Segel system with logistic source is considered. Under some conditions, we show that there exist initial data such that the smooth local-in-time solution of the system blows up in finite time, and thus the superlinear growth restrictions is insufficient to rule out the chemotactic collapse os the solution.