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On the hydrodynamical limit for a one dimensional kinetic model of cell aggregation by chemotaxis

Abstract : The hydrodynamic limit of a one dimensional kinetic model describing chemotaxis is investigated. The limit system is a conservation law coupled to an elliptic problem for which the macroscopic velocity is possibly discontinuous. Therefore, we need to work with measure-valued densities. After recalling a blow-up result in finite time of regular solutions for the hydrodynamic model, we establish a convergence result of the solutions of the kinetic model towards solutions of a problem limit defined thanks to the flux. Numerical simulations illustrate this convergence result.
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Contributor : Francois James <>
Submitted on : Monday, October 18, 2010 - 8:27:30 PM
Last modification on : Monday, May 11, 2020 - 6:14:08 PM
Document(s) archivé(s) le : Wednesday, January 19, 2011 - 2:55:09 AM

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  • HAL Id : hal-00527338, version 1
  • ARXIV : 1010.3683

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Francois James, Nicolas Vauchelet. On the hydrodynamical limit for a one dimensional kinetic model of cell aggregation by chemotaxis. Rivista di Matematica della Università di Parma, Istituto di Matematica, 2012, 3 (1), pp.91-113. ⟨hal-00527338⟩

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