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Journal of Mathematical Biology

, Volume 51, Issue 6, pp 595–615 | Cite as

Kinetic models for chemotaxis: Hydrodynamic limits and spatio-temporal mechanisms

  • Y. DolakEmail author
  • C. Schmeiser
Article

Abstract

We study kinetic models for chemotaxis, incorporating the ability of cells to assess temporal changes of the chemoattractant concentration as well as its spatial variations. For prescribed smooth chemoattractant density, the macroscopic limit is carried out rigorously. It leads to a drift equation with a chemotactic sensitivity depending on the time derivative of the chemoattractant density. As an application it is shown by numerical experiments that the new model can resolve the chemotactic wave paradox. For this purpose, the macroscopic equation is coupled to a simple activation-inhibition model for the chemoattractant which produces the chemoattractant waves typical for the slime mold Dictyostelium discoideum.

Keywords or Pharses

Chemotaxis Transport equations Aggregation Macroscopic limit 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of SciencesAustria
  2. 2.Vienna University of Technology Institute for Analysis and Scientific ComputingWienAustria

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