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

Vincent Calvez, José A. Carrillo

Research output: Contribution to journalArticleResearchpeer-review

141 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 languageEnglish
Pages (from-to)155-175
JournalJournal des Mathematiques Pures et Appliquees
Volume86
Issue number2
DOIs
Publication statusPublished - 1 Aug 2006

Keywords

  • A priori estimates
  • Chemotaxis
  • Prevention of overcrowding
  • Volume effect

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