Stable blow-up dynamic for the parabolic-parabolic Patlak-Keller-Segel   model
  We consider the parabolic-parabolic two-dimensional Patlak-Keller-Segel problem. We prove the existence of stable blow-up dynamics in finite time in the radial case. We extend in this article the result of [36] for the parabolic-elliptic case. 
Remi Schweyer
math.AP