Francesca Marcellini

A 2-Phase Traffic Model Based on a Speed Bound

We extend the classical Lighthill–Whitham–Richards (LWR) traffic model allowing different maximal speeds for different vehicles. Then we add a uniform bound on the traffic speed. The result, presented in this paper, is a new macroscopic model displaying two phases based on a nonsmooth

A mixed ODE–PDE model for vehicular traffic

2\times2

A traffic model aware of real time data

system of conservation laws. This model is compared with other models of the same type in the current literature, as well as with a kinetic one. Moreover, we establish a rigorous connection between a microscopic follow-the-leader model based on ordinary differential equations and this macroscopic continuum model.

The Godunov Method for a 2-Phase Model

We present a traffic flow model consisting of a gluing between the Lighthill–Whitham and Richards macroscopic model with a first-order microscopic following the leader model. The basic analytical properties of this model are investigated. Existence and uniqueness are proved, as well as the basic estimates on the dependence of solutions from the initial data. Moreover, numerical integrations show some qualitative features of the model, in particular the transfer of information among regions where the different models are used. Copyright

Modeling and analysis of pooled stepped chutes

Nowadays, traffic monitoring systems have access to real time data, e.g. through GPS devices. We propose a new traffic model able to take into account these data and, hence, able to describe the effects of unpredictable accidents. The well-posedness of this model is proved and numerical integrations show qualitative features of the resulting solutions. As a further motivation for the use of real time data, we show that the inverse problem for the Lighthill–Whitham and Richards (LWR) model is ill-posed.

Coupling conditions for the

Abstract We consider the Godunov numerical method to the phase-transition trafic model, proposed in [1], by Colombo, Marcellini, and Rascle. Numerical tests are shown to prove the validity of the method. Moreover we highlight the differences between such model and the one proposed in [2], by Blandin, Work, Goatin, Piccoli, and Bayen.

3\times 3

We consider a mathematical model describing pooled stepped chutes where the transport in each pooled step is described by the shallow-water equations. Such systems can be found for example at large dams in order to release overflowing water. We analyze the mathematical conditions coupling the flows between different chutes taken from the engineering literature. For the case of two canals divided by a weir, we present the solution to the Riemann problem for any initial data in the subcritical region, moreover we give a well-posedness result. We finally report on some numerical experiments.

Euler system

This paper is devoted to the extension to the full

On the stability of a model for the cutting of metal plates by means of laser beams

3\times3

Smooth and Discontinuous Junctions in the p-System

Euler system of the basic analytical properties of the equations governing a fluid flowing in a duct with varying section. First, we consider the Cauchy problem for a pipeline consisting of 2 ducts joined at a junction. Then, this result is extended to more complex pipes. A key assumption in these theorems is the boundedness of the total variation of the pipes section. We provide explicit examples to show that this bound is necessary.