We present a multilane traffic model based on balance laws, where the nonlocal source term is used to describe lane changing rate. The modelling framework includes consideration of local and flux functions. Based Godunov type numerical scheme, we provide BV estimates discrete entropy inequality. Together with $L^1$-contractivity property, prove existence uniqueness weak solutions. Numerical exa...

We establish that, for a Markov semi-group, $L^2$ hypocoercivity, i.e. contractivity modified norm, implies quantitative deviation bounds additive functionals of the associated process and exponential integrability hitting time sets with positive measure. Moreover, in case diffusion processes under strong hypoellipticity assumption, we prove that hypocoercivity existence Lyapunov function gener...

We present synchronization and contractivity estimates for the kinetic Kuramoto model obtained from the Kuramoto phase model in the mean-field limit. For identical Kuramoto oscillators, we present an admissible class of initial data leading to time-asymptotic complete synchronization, that is, all measure valued solutions converge to the traveling Dirac measure concentrated on the initial avera...

A basic result in semigroup theory states that every C0-semigroup is quasi-contractive with respect to some appropriately chosen equivalent norm. This paper contains a counterpart of this well-known fact. Namely, by examining the convergence of the Trotter-type formula (e t n P ) (where P denotes a bounded projection), we prove that whenever the generator A is unbounded it is possible to introd...

Article history: Received 16 January 2014 Accepted 20 September 2014 Available online 22 October 2014 Submitted by Y. Wei MSC: 15A18 15A57

The long time behavior of the random map xn → xn+1 = |xn − θn| is studied under various assumptions on the distribution of the θn. One of the interesting features of this random dynamical system is that for a single fixed deterministic θ the map is not a contraction, while the composition is almost surely a contraction if θ is chosen randomly with only mild assumptions on the distribution of th...