On a linear runs and tumbles equation

S Mischler; Q Weng

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arXiv · 1602.03474

On a linear runs and tumbles equation

S Mischler·Q Weng

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Abstract

We consider a linear runs and tumbles equation in dimension d $\ge$ 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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S Mischler, Q Weng. 2016-02-10. On a linear runs and tumbles equation. https://arxiv.org/abs/1602.03474

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