Confinement by biased velocity jumps: aggregation of Escherichia coli

Abstract : We investigate a linear kinetic equation derived from a velocity jump process modelling bacterial chemotaxis in the presence of an external chemical signal centered at the origin. We prove the existence of a positive equilibrium distribution with an exponential decay at infinity. We deduce a hypocoercivity result, namely: the solution of the Cauchy problem converges exponentially fast towards the stationary state. The strategy follows [J. Dolbeault, C. Mouhot, and C. Schmeiser, Hypocoercivity for linear kinetic equations conserving mass, Trans. AMS 2014]. The novelty here is that the equilibrium does not belong to the null spaces of the collision operator and of the transport operator. From a modelling viewpoint it is related to the observation that exponential confinement is generated by a spatially inhomogeneous bias in the velocity jump process.
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Submitted on : Wednesday, April 2, 2014 - 4:48:30 PM
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  • HAL Id : hal-00971302, version 1
  • ARXIV : 1404.0643

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Vincent Calvez, Gaël Raoul, Christian Schmeiser. Confinement by biased velocity jumps: aggregation of Escherichia coli. Kinetic and Related Models , AIMS, 2015. ⟨hal-00971302⟩

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