## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- Electronic Research Announcements
- Conference Publications
- AIMS Mathematics

NHM

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 telecommunication case, by using the
model introduced by D'Apice-Manzo-Piccoli and, finally, the
case of a gas pipeline, modeled by the classical $p$-system.
For each of these models we present a review of some results about Riemann
and Cauchy problems in the case of a network, formed by a single vertex
with $n$ incoming and $m$ outgoing arcs.

PROC

We consider $n$ tubes exiting a junction and filled with a non
viscous isentropic or isothermal fluid. In each tube a copy of the
$p$-system in Euler coordinates is considered. The aim of the
presentation is to compare three different notions of solutions at
the junctions: p-solutions, Q-solutions and P-solutions.

NHM

The aim of this paper is to address the following questions: which models,
among fluido-dynamic ones, are more appropriate to describe urban traffic?
While a rich debate was developed for the complicate
dynamics of highway traffic, some
basic problems of urban traffic are not always appropriately discussed.
We analyze many recent, and less recent, models focusing on three
basic properties.
The latter are necessary to reproduce correctly queue formation at lights and
junctions, and their backward propagation on an urban network.

MBE

We prove existence and uniqueness of solutions, continuous
dependence from the initial datum and stability with respect to the
boundary condition in a class of initial--boundary value problems
for systems of balance laws. The particular choice of the boundary
condition allows to comprehend models with very different
structures. In particular, we consider a juvenile-adult model, the
problem of the optimal mating ratio and a model for the optimal
management of biological resources. The stability result obtained
allows to tackle various optimal management/control problems,
providing sufficient conditions for the existence of optimal
choices/controls.

DCDS

We consider the Lighthill-Whitham-Richards traffic flow model
on a network composed by an arbitrary number of incoming and
outgoing arcs connected together by a node with a buffer.
Similar to [15],
we define the solution to the Riemann problem at the node
and we prove existence
and well posedness of solutions to the Cauchy problem,
by using the wave-front tracking technique and the generalized tangent
vectors.

NHM

We consider a hyperbolic conservation law with discontinuous flux. Such a partial differential equation arises in different applications, 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 corresponding weak entropic solutions.

DCDS-S

We consider the Lighthill-Whitham-Richards traffic flow model
on a network composed by a single junction $J$ with $n$ incoming roads,
$m$ outgoing roads and $m$ buffers, one for each outgoing road.
We introduce a concept solution at $J$, which is compared with that
proposed in [14]. Finally we study the Cauchy problem and,
in the special case of $n \le 2$ and $m \le 2$, we prove existence
of solutions to the Cauchy problem, via the wave-front tracking method.

keywords:
junction
,
Lighthill-Whitham-Richards model
,
Conservation laws
,
multibuffer
,
traffic problems.

NHM

This paper deals with coupling conditions between the
classical microscopic Follow The Leader model and a
phase transition (PT) model.
We propose a solution at the interface
between the two models.
We describe the solution to the Riemann problem.

NHM

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 hold
in the standard case.

DCDS

In this paper, we investigate the connections between
controllability 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 $n\geq
2$, the steady--state controllability for the heat equation with
boundary controls dependent only on time, does not hold. In a
second step, we study a model of a water tank whose dynamics is
given by a wave equation on a two-dimensional bounded open domain.
We provide a condition which prevents steady-state
controllability of such a system, where the control acts on the
boundary and is only dependent on time. Using that condition, we
prove that the steady-state controllability does not hold for
generic tank shapes.

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]