Kinetic models for chemotaxis and their drift-diffusion limits

Fabio A.C.C. Chalub*, Peter Markowich, Benoît Perthame, Christian Schmeiser

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

156 Scopus citations

Abstract

Kinetic models for chemotaxis, nonlinearly coupled to a Poisson equation for the chemo-attractant density, are considered. Under suitable assumptions on the turning kernel (including models introduced by Othmer, Dunbar and Alt), convergence in the macroscopic limit to a drift-diffusion model is proven. The drift-diffusion models derived in this way include the classical Keller-Segel model. Furthermore, sufficient conditions for kinetic models are given such that finite-time-blow-up does not occur. Examples are given satisfying these conditions, whereas the macroscopic limit problem is known to exhibit finite-time-blow-up. The main analytical tools are entropy techniques for the macroscopic limit as well as results from potential theory for the control of the chemo-attractant density.

Original languageEnglish (US)
Pages (from-to)123-141
Number of pages19
JournalMonatshefte fur Mathematik
Volume142
Issue number1-2
DOIs
StatePublished - Jan 1 2004

Keywords

  • Chemotaxis
  • Drift-diffusion limits
  • Kinetic models

ASJC Scopus subject areas

  • Mathematics(all)

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