On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher
Blanchet, Adrien
HAL, hal-00620500 / Harvested from HAL
Text on HAL
This review is dedicated to recent results on the 2d parabolic-elliptic Patlak-Keller-Segel model, and on its variant in higher dimensions where the diffusion is of critical porous medium type. Both of these models have a critical mass $M_c$ such that the solutions exist globally in time if the mass is less than $M_c$ 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. A number of open questions are also stated.
Publié le : 2011-09-07
Classification:  entropy methods,  Chemotaxis,  Patlak-Keller-Segel model,  aggregation,  blowup,  entropy methods.,  Primary: 35B44, 35A01; Secondary: 35B40, 35B33, 35Q92,  [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] 
@article{hal-00620500,
     author = {Blanchet, Adrien},
     title = {On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher},
     journal = {HAL},
     volume = {2011},
     number = {0},
     year = {2011},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00620500}
}

Blanchet, Adrien. On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher. HAL, Tome 2011 (2011) no. 0, . http://gdmltest.u-ga.fr/item/hal-00620500/