RT Journal Article
SR 00
A1 Blanchet, Adrien
T1 A gradient flow approach to the Keller-Segel systems
JF RIMS Kokyuroku's lecture note
YR 2013
FD 2013-06
VO vol.1837
SP 52
OP 73
K1 chemo-taxis
K1 Keller-Segel model
K1 degenerate diffusion
K1 minimising scheme
K1 Monge-Kantorovich distance
AB These notes are dedicated to recent global existence and regularity results on the parabolic-elliptic Keller-Segel model in dimension 2, and its generalisation with nonlinear diffusion in higher dimensions, obtained throught a gradient flow approach in the Wassertein metric. These models have a critical mass Mc such that the solutions exist globally in time if the mass is less than Mc and above which there are solutions which blowup in finite time. The main tools, in particular the free energy, and the idea of the methods are set out.
PB Kyoto University
SN 1881-6193
LK https://publications.ut-capitole.fr/id/eprint/16518/
UL http://tse-fr.eu/pub/28180