Abstract:
Recently,
Berthelin, Degond, Delitala and Rascle introduced a traffic
flow model describing the formation and the dynamics of traffic jams.
This model which consists of a Constrained Pressureless Gas Dynamics
system assumes that the maximal density constraint is independent of
the velocity. However, in practice, the distribution of vehicles on a
highway depends on their velocity. In this paper we propose a more
realistic model namely the Second Order Model with Constraint
(SOMC model), derived from the Aw & Rascle model,
which takes into account this feature. Moreover, when the maximal
density constraint is saturated, the SOMC model ``relaxes'' to the
Lighthill & Whitham model. We prove an existence
result of weak solutions for this model by means of cluster dynamics in
order to construct a sequence of approximations and we solve completely
the associated Riemann problem.