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Chemotaxis: from kinetic equations to aggregate dynamics

  • F. JamesEmail author
  • N. Vauchelet
Article

Abstract

The hydrodynamic limit for a kinetic model of chemotaxis is investigated. The limit equation is a non local conservation law, for which finite time blow-up occurs, giving rise to measure-valued solutions and discontinuous velocities. An adaptation of the notion of duality solutions, introduced for linear equations with discontinuous coefficients, leads to an existence result. Uniqueness is obtained through a precise definition of the nonlinear flux as well as the complete dynamics of aggregates, i.e. combinations of Dirac masses. Finally a particle method is used to build an adapted numerical scheme.

Mathematics Subject Classification (2010)

35B40 35D30 35L60 35Q92 

Keywords

Duality solutions Non local conservation equations Hydrodynamic limit Measure-valued solutions Chemotaxis 

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Mathématiques, Analyse, Probabilités, Modélisation, Orléans (MAPMO)CNRS UMR 7349 and Fédération Denis Poisson, CNRS FR 2964, Université d’Orléans and CNRSOrléans Cedex 2France
  2. 2.UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions CNRS, UMR 7598Laboratoire Jacques-Louis Lions and INRIA Paris-RocquencourtParisFrance

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