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- Giuseppe Maria Coclite, Mauro Garavello, Benedetto Piccoli
- SIAM J. Math. Analysis
- 2005

This paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from conservation of the number of cars, defined on a road network that is a collection of roads with junctions. The evolution problem is underdetermined at junctions, hence we choose to have some fixed rules for the… (More)

We consider an hyperbolic conservation law with discontinuous flux. Such partial differential equation arises in different applicative problems, in particular we are motivated by a model of traffic flow. We provide a new formulation in terms of Riemann Solvers. Moreover, we determine the class of Riemann Solvers which provide existence and uniqueness of the… (More)

- Rinaldo M. Colombo, Mauro Garavello
- NHM
- 2006

- Rinaldo M. Colombo, Mauro Garavello
- SIAM J. Math. Analysis
- 2008

- Mauro Garavello, Benedetto Piccoli
- SIAM J. Control and Optimization
- 2005

We consider a hybrid control system and general optimal control problems for this system. We suppose that the switching strategy imposes restrictions on control sets and we provide necessary conditions for an optimal hybrid trajectory, stating a Hybrid Necessary Principle (HNP). Our result generalizes various necessary principles available in the… (More)

Consider a fluid flowing through a junction between two pipes with different sections. Its evolution is described by the 2D or 3D Euler equations, whose analytical theory is far from complete and whose numerical treatment may be rather costly. This note compares different 1D approaches to this phenomenon. Key words and phrases: p-system at junctions, fluid… (More)

Motivated by applications to the piston problem, to a manhole model, to blood flow and to supply chain dynamics, this paper deals with a system of conservation laws coupled with a system of ordinary differential equations. The former is defined on a domain with boundary and the coupling is provided by the boundary condition. For each of the examples… (More)

- Yacine Chitour, Jean–Michel Coron, Mauro Garavello
- 2005

In this paper, we investigate the connections between controllabil-ity properties of distributed systems and existence of non zero entire functions subject to restrictions on their growth and on their sets of zeros. Exploiting these connections, we first show that, for generic bounded open domains in dimension n ≥ 2, the steady–state controllability for the… (More)

- Mauro Garavello, Benedetto Piccoli
- NHM
- 2009

- Mauro Garavello
- NHM
- 2010

This paper deals with various applications of conservation laws on networks. In particular we consider the car traffic, described by the Lighthill-Whitham-Richards model and by the Aw-Rascle-Zhang model, the telecommu-nication case, by using the model introduced by D'Apice-Manzo-Piccoli and, finally, the case of a gas pipeline, modeled by the classical… (More)