Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium

Jaewook Ahn, Jae-Myoung Kim, Junha Kim

This paper studies the Cauchy problem for the fully parabolic Keller-Segel system. The main results show that there exists a critical threshold $A_{\mathrm{crit}}>0$ for steady states $…