On a linear runs and tumbles equation

Mischler, Stéphane; Weng, Qilong

Mischler, Stéphane; Weng, Qilong (2017), On a linear runs and tumbles equation, Kinetic & Related Models, 10, 3, p. 799 - 822. 10.3934/krm.2017032

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Type

Article accepté pour publication ou publié

Date

2017

Journal name

Kinetic & Related Models

Volume

Number

Publisher

American Institute of Mathematical Sciences

Pages

799 - 822

Abstract (EN)

We consider a linear runs and tumbles equation in dimension d≥1 for which we establish the existence of a unique positive and normalized steady state as well as its asymptotic stability, improving similar results obtained by Calvez et al. [8] in dimension d=1. Our analysis is based on the Krein-Rutman theory revisited in [23] together with some new moment estimates for proving confinement mechanism as well as dispersion, multiplicator and averaging lemma arguments for proving some regularity property of suitable iterated averaging quantities.

Subjects / Keywords

stationary state; chemotaxis; hypocoercivity; Kinetic equations; velocity-jump processes; asymptotic stability