On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher
type: Item
instance of: scholarly article
title: On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher
zbMATH Open document ID: 1326.35400
author: Adrien Blanchet
published in: Séminaire Laurent Schwartz. EDP et Applications
publication date: 2015-07-10T00:00:00Z
full work available at URL: https://arxiv.org/abs/1109.1543
full work available at URL: Blanchet 19676.pdf
review text: This is a review paper on recent results for the classical Keller-Segel model of chemotaxis in two space dimensions as well as for its higher dimensions analogs (involving nonlinear diffusion) that have a critical mass. Main results include blowup of solutions above the critical mass and fine asymptotics of solutions obtained using free energy functional and related entropy functionals. Open problems are also formulated.
reviewed by: Piotr Biler
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 92C17
zbMATH DE Number: 6457674
zbMATH Keywords: chemotaxis
zbMATH Keywords: Keller-Segel model
zbMATH Keywords: nonlinear diffusion
zbMATH Keywords: blowup
zbMATH Keywords: entropy methods
MaRDI profile type: Publication
OpenAlex ID: W2963706166
arXiv ID: 1109.1543
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On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher (cites work)
cites work: Q4805362

On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher (cites work)
cites work: Nonlinear Schrödinger equations and sharp interpolation estimates

On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher (DOI)
DOI: 10.5802/SLSEDP.6