On a linear runs and tumbles equation
Analysis of PDEs
2016-09-12 v3
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.
Cite
@article{arxiv.1602.03474,
title = {On a linear runs and tumbles equation},
author = {S Mischler and Q Weng},
journal= {arXiv preprint arXiv:1602.03474},
year = {2016}
}