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

Departamento de Matemáticas

Producción científica: Contribución a una revista › Artículo › Investigación › revisión exhaustiva

200 Citas (Scopus)

Resumen

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.

Idioma original	Inglés
Páginas (desde-hasta)	155-175
Publicación	Journal des Mathematiques Pures et Appliquees
Volumen	86
N.º	2
DOI	https://doi.org/10.1016/j.matpur.2006.04.002
Estado	Publicada - 1 ago 2006

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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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AU - Calvez, Vincent

AU - Carrillo, José A.

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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

UR - https://www.scopus.com/pages/publications/33746377577

U2 - 10.1016/j.matpur.2006.04.002

DO - 10.1016/j.matpur.2006.04.002

M3 - Article

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SP - 155

EP - 175

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

IS - 2

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

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