Jose Antonio Carrillo, ICREA and the Universitat Autonoma de Barcelona
The Patlak-Keller-Segel model: free energies, geometric inequalities and gradient flows
The long-time asymptotics of this well-known model in chemotaxis cell movement will be analyzed in the critical case. Its connection to free energies and the logarithmic HLS inequality will lead to the proof of infinite time aggregation in the critical case. A similar problem with nonlinear diffusion exhibiting analogous behavior will be studied in any dimensions. This corresponds to two works in collaboration with A. Blanchet and N. Masmoudi and A. Blanchet and P. Laurencot respectively.
TUESDAY, April 22, 2008