On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher

Adrien Blanchet[1]

  • [1] Toulouse School of Economics (GREMAQ, Université de Toulouse) 21 Allée de Brienne F-31000 Toulouse France

Séminaire Laurent Schwartz — EDP et applications (2011-2012)

  • Volume: 2011-2012, page 1-26
  • ISSN: 2266-0607

Abstract

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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.

How to cite

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Blanchet, Adrien. "On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher." Séminaire Laurent Schwartz — EDP et applications 2011-2012 (2011-2012): 1-26. <http://eudml.org/doc/251170>.

@article{Blanchet2011-2012,
abstract = {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.},
affiliation = {Toulouse School of Economics (GREMAQ, Université de Toulouse) 21 Allée de Brienne F-31000 Toulouse France},
author = {Blanchet, Adrien},
journal = {Séminaire Laurent Schwartz — EDP et applications},
keywords = {chemotaxis; Keller-Segel model; nonlinear diffusion; blowup; entropy methods},
language = {eng},
pages = {1-26},
publisher = {Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher},
url = {http://eudml.org/doc/251170},
volume = {2011-2012},
year = {2011-2012},
}

TY - JOUR
AU - Blanchet, Adrien
TI - On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher
JO - Séminaire Laurent Schwartz — EDP et applications
PY - 2011-2012
PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2011-2012
SP - 1
EP - 26
AB - 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.
LA - eng
KW - chemotaxis; Keller-Segel model; nonlinear diffusion; blowup; entropy methods
UR - http://eudml.org/doc/251170
ER -

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