Volume effects in the Keller-Segel model: energy estimates preventing blow-up

Vincent Calvez; José A. Carrillo

doi:10.1016/j.matpur.2006.04.002

Volume effects in the Keller-Segel model: energy estimates preventing blow-up

Vincent Calvez, José A. Carrillo

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

156 Citations (Scopus)

Abstract

We obtain a priori estimates for the classical chemotaxis model of Patlak, Keller and Segel when a nonlinear diffusion or a nonlinear chemosensitivity is considered accounting for the finite size of the cells. We will show how entropy estimates give natural conditions on the nonlinearities implying the absence of blow-up for the solutions. © 2006 Elsevier SAS. All rights reserved.

Original language	English
Pages (from-to)	155-175
Journal	Journal des Mathematiques Pures et Appliquees
Volume	86
Issue number	2
DOIs	https://doi.org/10.1016/j.matpur.2006.04.002
Publication status	Published - 1 Aug 2006

Keywords

A priori estimates
Chemotaxis
Prevention of overcrowding
Volume effect

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10.1016/j.matpur.2006.04.002

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title = "Volume effects in the Keller-Segel model: energy estimates preventing blow-up",

abstract = "We obtain a priori estimates for the classical chemotaxis model of Patlak, Keller and Segel when a nonlinear diffusion or a nonlinear chemosensitivity is considered accounting for the finite size of the cells. We will show how entropy estimates give natural conditions on the nonlinearities implying the absence of blow-up for the solutions. {\textcopyright} 2006 Elsevier SAS. All rights reserved.",

keywords = "A priori estimates, Chemotaxis, Prevention of overcrowding, Volume effect",

author = "Vincent Calvez and Carrillo, {Jos{\'e} A.}",

year = "2006",

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T1 - Volume effects in the Keller-Segel model: energy estimates preventing blow-up

AU - Calvez, Vincent

AU - Carrillo, José A.

PY - 2006/8/1

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N2 - We obtain a priori estimates for the classical chemotaxis model of Patlak, Keller and Segel when a nonlinear diffusion or a nonlinear chemosensitivity is considered accounting for the finite size of the cells. We will show how entropy estimates give natural conditions on the nonlinearities implying the absence of blow-up for the solutions. © 2006 Elsevier SAS. All rights reserved.

AB - We obtain a priori estimates for the classical chemotaxis model of Patlak, Keller and Segel when a nonlinear diffusion or a nonlinear chemosensitivity is considered accounting for the finite size of the cells. We will show how entropy estimates give natural conditions on the nonlinearities implying the absence of blow-up for the solutions. © 2006 Elsevier SAS. All rights reserved.

KW - A priori estimates

KW - Chemotaxis

KW - Prevention of overcrowding

KW - Volume effect

U2 - 10.1016/j.matpur.2006.04.002

DO - 10.1016/j.matpur.2006.04.002

M3 - Article

SN - 0021-7824

VL - 86

SP - 155

EP - 175

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

IS - 2

ER -

Volume effects in the Keller-Segel model: energy estimates preventing blow-up

Abstract

Keywords

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