| Program | (subject to changes!) |
|---|---|
| 10:30-11:00 |
The LWR model on a network with generic junctions
Mauro Garavello Dipartimento di Scienze e Tecnologie Avanzate Università del Piemonte Orientale "A. Avogadro" AbstractThe Lighthill-Whitham-Richards (LWR) is a model for the description of the evolution of car traffic. It is based on the conservation of the number of cars and it consists on the nonlinear hyperbolic equation $\rho_t+f(\rho)_x=0$, where $\rho(t,x)$ denotes the density of cars in a road, modeled by a real interval, $f(\rho)=v(\rho)\cdot\rho$ is the flux function and $v(\rho)$ is the average speed of cars. We consider a network, composed by a finite number of roads connected together by junctions, and Riemann problems at junctions. A junction $J$ is modeled by a finite set of incoming roads and by a finite set of outgoing roads. Instead a Riemann problem at $J$ is simply a Cauchy problem with constant initial data in each road of $J$. We present some different ways to solve Riemann problems at $J$. Moreover we deal with the Cauchy problem on the whole network. In order to prove existence of solutions to the Cauchy problem, we construct wave-front tracking approximate solutions, converging in $BV$-norm to a function, which is indeed a solution. It is clear that these approximate solutions depend on the Riemann solver at the junctions. We are able to prove that, under general hypotheses on the Riemann solver, a solution to the Cauchy problem exists for every positive time. The main novelty is that we do not restrict to the case of a particular Riemann solver and of simple junctions. |
| 11:00-11:30 |
Traffic Flow Modelling with Junctions from a Multiclass Point of View
Magali Mercier Université Lyon I AbstractMotivated by the modeling of a roundabout, we are led to study the traffic on a road with points of entry and exit. In this talk, we would like to describe a junction and solve the Riemann problem for such a model.In the case of the one-T road, we obtain a result of existence and uniqueness. This first step allows us to obtain a similar result for the n-T road. We will describe these results and also some properties of the obtained solutions, in order to see how long this model is valid. |
| Coffe Break | |
| 12:00-12:30 |
Flow control in gas networks: Exact controllability to a given demand
Veronika Schleper Technische Universität Kaiserslautern AbstractWe consider a network of pipelines where the flow is controlled by a number of compressors. The customer demand is described by desired boundary traces of the system state. We seek compressor control functions such that this demand (and possibly also certain supply constraints) are fulfilled. In the framework of continuously differentiable states, we present an explicit construction of these control functions, which can also be used as a fast non--iterative algorithm for numerical computations. |
| 12:30-13:00 |
Smooth and Discontinuous Junctions in Gas Pipelines
Francesca Marcellini Dipartimento di Matematica e Applicazioni Università di Milano - Bicocca AbstractWe consider the dynamics of a non viscous isentropic or isothermal fluid filling tube with a junction. Two different approaches are presented: a pipe with varying section a(x) Lipschitz continuous and the case of a sharp change in the pipe' section. We rigorously prove that as the section a(x) tends to the step function, then the solution to the first problem converge to solutions of the latter one. |
| Lunch Break | |
| 15:00-15:30 |
Solutions with Large Total Variation to Nonconservative Hyperbolic Systems
Francesca Monti Dipartimento di Matematica e Applicazioni Università di Milano - Bicocca Abstract |
| 15:30-16:00 |
On Continuum Models for Pedestrian Flows
Massimiliano D. Rosini Dipartimento di Matematica Università degli Studi di Brescia AbstractThis talk will present some recent results on continuum models for pedestrian flows. Some effects of panicking situations can be described through a 1D model, whose analytical properties will be described. |
| 16:00-16:30 |
A new continuum model for crowd dynamics
Giancarlo Facchi Università degli Studi di Brescia AbstractWe show some results related to the numerical integration of a model that describes the evacuation of a room. |
Organizers: Rinaldo M. Colombo, Graziano Guerra, Massimiliano D. Rosini