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Chemotaxis: from kinetic equations to aggregate dynamics

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.
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https://hal.archives-ouvertes.fr/hal-00605479
Contributor : Francois James <>
Submitted on : Friday, December 2, 2011 - 12:18:23 PM
Last modification on : Monday, May 11, 2020 - 6:14:03 PM
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François James, Nicolas Vauchelet. Chemotaxis: from kinetic equations to aggregate dynamics. Nonlinear Differential Equations and Applications, Springer Verlag, 2013, 20 (1), pp.101-127. ⟨10.1007/s00030-012-0155-4⟩. ⟨hal-00605479v3⟩

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