Global boundedness and asymptotic stability of the Keller-Segel system with logistic-type source in the whole space

Qingchun Li, Haomeng Chen

In this paper, we investigate the Cauchy problem of the parabolic-parabolic Keller-Segel system with the logistic-type term $au-b{u}^3$ on ${\mathbb{R}}^N,N\ge 2$. We discuss the glo…