Abstract:
In this paper, we establish and
analyze a traffic flow model which
describes the formation and dynamics of traffic jams. It 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.
From this analysis, we deduce the particular dynamical behaviour of
clusters (or traffic jams), defined as intervals where the density
limit is reached. An existence result for a generic class of initial
data is proven by means of an approximation of the solution by a
sequence of clusters. Finally, numerical simulations are produced.