A model for the evolution of traffic jams in multi-lane
Florent Berthelin Damien Broizat
In [8], Berthelin, Degond, Delitala and Rascle introduced a traffic flow model describing the formation and the dynamics of traffic jams. This model consists of a Pressureless Gas Dynamics system under a maximal constraint on the density and is derived through a singular limit of the Aw-Rascle model. In the present paper we propose an improvement of this model by allowing the road to be multi-lane piecewise. The idea is to use the maximal constraint to model the number of lanes. We also add in the model a parameter $\alpha$ which model the various speed limitations according to the number of lanes. We present the dynamical behaviour of clusters (traffic jams) and by approximation with such solutions, we obtain an existence result of weak solutions for any initial data.
keywords: Traffic flow models weak solutions constrained pressureless gas dynamics traffic jams. multi-lane
Convergence rate for the method of moments with linear closure relations
Yves Bourgault Damien Broizat Pierre-Emmanuel Jabin
We study linear closure relations for the moments' method applied to simple kinetic equations. The equations are linear collisional models (velocity jump processes) which are well suited to this type of approximation. In this simplified, 1 dimensional setting, we are able to prove stability estimates for the method (with a kinetic interpretation by a BGK model). Moreover we are also able to obtain convergence rates which automatically increase with the smoothness of the initial data.
keywords: stability analysis. hyperbolicity method of moments Kinetic theory spectral type convergence closure relation

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