Asymptotic profile with the optimal convergence rate for a parabolic equation of chemotaxis in super-critical cases

By S. Luckhaus, Yoshie Sugiyama. 2007

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Nondegeneracy of blow-up points for the parabolic Keller–Segel system (2014, background): “When the chemosensitivity function φ(s) behaves for large s like s with m > 2/N , blow-up in finite time occurs independently of the magnitude of initial mass provided the data are concentrated enough, whereas all solutions exist globally if m < 2/N (see [12,29,35,45]).”
On the global existence of solutions to an aggregation model (2008, result): “The similar problem with f(n) = nm (m ‚ 0) and the parameter ´ = ´(n) = nqi2 (with q su‐ciently small) and › = IRd was studied recently in [ 25 ], where the authors studied the asymptotic behaviour”
Global strong solution to the semi-linear Keller-Segel system of parabolic-parabolic type with small data in scale invariant spaces (2009, background): “[16] H. Kozono, Y. Sugiyama, Local existence and finite time blow-up in the 2-”