A model for the evolution of trac jams in multi-lane

In [8], Berthelin, Degond, Delitala and Rascle introduced a trac ow model describing the formation and the dynamics of trac 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 which model the various speed limitations according to the number of lanes. We present the dynamical behaviour of clusters (trac jams) and by approximation with such solutions, we obtain an existence result of weak solutions for any initial data.