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ON A LINEAR RUNS AND TUMBLES EQUATION

Abstract : 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. [5] in dimension d = 1. Our analysis is based on the Krein-Rutman theory revisited in [18] 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.
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https://hal.archives-ouvertes.fr/hal-01272429
Contributor : Stéphane Mischler <>
Submitted on : Friday, September 9, 2016 - 12:36:03 PM
Last modification on : Tuesday, December 8, 2020 - 10:32:13 AM
Long-term archiving on: : Saturday, December 10, 2016 - 1:07:57 PM

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  • HAL Id : hal-01272429, version 3
  • ARXIV : 1602.03474

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Stéphane Mischler, Q Weng. ON A LINEAR RUNS AND TUMBLES EQUATION. Kinetic and Related Models , AIMS, 2017, 10 (3). ⟨hal-01272429v3⟩

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