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On a linear runs and tumbles equation

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KineticKSarxiv.pdf (390.1Kb)
Date
2017
Dewey
Analyse
Sujet
stationary state; chemotaxis; hypocoercivity; Kinetic equations; velocity-jump processes; asymptotic stability
Journal issue
Kinetic & Related Models
Volume
10
Number
3
Publication date
2017
Article pages
799 - 822
Publisher
American Institute of Mathematical Sciences
DOI
http://dx.doi.org/10.3934/krm.2017032
URI
https://basepub.dauphine.fr/handle/123456789/17132
Collections
  • CEREMADE : Publications
Metadata
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Author
Mischler, Stéphane
Weng, Qilong
Type
Article accepté pour publication ou publié
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.

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