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arXiv · 1404.0643

Confinement by biased velocity jumps: aggregation of Escherichia coli

Vincent Calvez·Gaël Raoul·Christian Schmeiser
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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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Vincent Calvez, Gaël Raoul, Christian Schmeiser. 2014-04-02. Confinement by biased velocity jumps: aggregation of Escherichia coli. https://arxiv.org/abs/1404.0643

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