TY  - JOUR
ID  - publications16518
UR  - http://tse-fr.eu/pub/28180
A1  - Blanchet, Adrien
Y1  - 2013/06//
N2  - 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
JF  - RIMS Kokyuroku's lecture note
VL  - vol.1837
KW  - chemo-taxis
KW  - Keller-Segel model
KW  - degenerate diffusion
KW  - minimising scheme
KW  - Monge-Kantorovich distance
SN  - 1881-6193
TI  - A gradient flow approach to the Keller-Segel systems
SP  - 52
AV  - public
EP  - 73
ER  -