This paper provides a mathematical model of the phenomenon of phase transitions in traffic
flow. The model consists of a scalar conservation law coupled with a 2× 2 system of …

We present an-population generalization of the Lighthill–Whitham and Richards traffic flow
model. This model is analytically interesting because of several non-standard features. For …

This work is devoted to the solution to Riemann Problems for the p-system at a junction, the
main goal being the extension to the case of an ideal junction of the classical results that …

We present a model for the description of a nonviscous isentropic or isothermal fluid
crossing a junction. Aiming at an extension of the usual Euler equations, we neglect the …

This paper deals with 2*2 conservation laws at a junction. For the Cauchy problem,
existence, uniqueness, and Lipschitz continuous dependence of the solution from the initial …

Mobile sensing enabled by GPS or smart phones has become an increasingly important
source of traffic data. For sufficient coverage of the traffic stream, it is important to maintain a …

This note is devoted to the study of traffic flow models that develop phase transitions. From
the analytical point of view, this is a first example of a well posedness result for conservation …

Consider the p-system describing the subsonic flow of a fluid in a pipe with section a= a (x).
We prove that the resulting Cauchy problem generates a Lipschitz semigroup, provided the …

In this work we analyze the reactive Riemann problem for thermally perfect gases in the
deflagration or detonation regimes. We restrict our attention to the case of one irreversible …

Consider the p-system with a general two phase fluid pressure law. Under an abstract
compatibility condition on subsonic phase boundaries we construct a Riemann Solver for …