Abstract:
Recently, 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 modelize the number of lanes.
We also add in the model a parameter $\alpha$ which modelize 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.