On a linear runs and tumbles equation
Mischler, Stéphane; Weng, Qilong (2017), On a linear runs and tumbles equation, Kinetic & Related Models, 10, 3, p. 799 - 822. 10.3934/krm.2017032
TypeArticle accepté pour publication ou publié
Journal nameKinetic & Related Models
American Institute of Mathematical Sciences
799 - 822
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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.  in dimension d=1. Our analysis is based on the Krein-Rutman theory revisited in  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 / Keywordsstationary state; chemotaxis; hypocoercivity; Kinetic equations; velocity-jump processes; asymptotic stability
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Special modes and hypocoercivity for linear kinetic equations with several conservation laws and a confining potential Carrapatoso, Kleber; Dolbeault, Jean; Hérau, Frédéric; Mischler, Stéphane; Mouhot, Clément; Schmeiser, Christian (2021) Document de travail / Working paper