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September  2010, 3(3): 501-528. doi: 10.3934/krm.2010.3.501

Numerical simulation of a kinetic model for chemotaxis

Nicolas Vauchelet 1,

1. 

UPMC, Univ Paris 06, UMR 7598 LJLL, Paris F-75005 France, CNRS, UMR 7598 LJLL, Paris, F-75005, France

Received  September 2009 Revised  March 2010 Published  July 2010

This paper is devoted to numerical simulations of a kinetic model describing chemotaxis. This kinetic framework has been investigated since the 80's when experimental observations have shown that the motion of bacteria is due to the alternance of 'runs and tumbles'. Since parabolic and hyperbolic models do not take into account the microscopic movement of individual cells, kinetic models have become of a great interest. Dolak and Schmeiser (2005) have then proposed a kinetic model describing the motion of bacteria responding to temporal gradients of chemoattractants along their paths. An existence result for this system is provided and a numerical scheme relying on a semi-Lagrangian method is presented and analyzed. An implementation of this scheme allows to obtain numerical simulations of the model and observe blow-up patterns that differ greatly from the case of Keller-Segel type of models.
Keywords: Kinetic equations, semi-Lagrangian method, Chemotaxis, convergence analysis..
Mathematics Subject Classification: Primary: 92C17, 92B05; Secondary: 65M12, 82C8.
Citation: Nicolas Vauchelet. Numerical simulation of a kinetic model for chemotaxis. Kinetic & Related Models, 2010, 3 (3) : 501-528. doi: 10.3934/krm.2010.3.501
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