ON A LINEAR RUNS AND TUMBLES EQUATION

Stéphane Mischler (1) , Q Weng (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

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

Domaines: Equations aux dérivées partielles [math.AP]

Stéphane Mischler, Q Weng. ON A LINEAR RUNS AND TUMBLES EQUATION. 2016. ⟨hal-01272429v2⟩