一类具有logistic源的高维Keller-Segel模型的爆破

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

摘要:

本文考虑一类带有logistic源项的Keller-Segel模型的Cauchy问题，在一定条件下证得问题的解在有限时间爆破. 这表明在高维情况下即便有logistic源项的存在也不能排除爆破的发生.

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.