Giuseppe Maria Coclite

Traffic flow on a road network

This paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from the 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 distribution of traffic plus optimization criteria for the flux. We prove existence of solutions to the Cauchy problem and we show that the Lipschitz continuous dependence by initial data does not hold in general, but it does hold under special assumptions.Our method is based on a wave front tracking approach [A. Bressan, Hyperbolic Systems of Conservation Laws. The One-dimensional Cauchy Problem, Oxford University Press, Oxford, UK, 2000] and works also for boundary data and time-dependent coefficients of traffic distribution at junctions, including traffic lights.

On the Boundary Control of Systems of Conservation Laws

This paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand, we give an example showing that exact controllability in finite time cannot be achieved, in general.

On the Attainable Set for Temple Class Systems with Boundary Controls

Consider the initial-boundary value problem for a strictly hyperbolic, genuinely nonlinear, Temple class system of conservation laws \begin{equation}\label{eq:1} u_t+f(u)_x=0, \qquad u(0,x)=\ov u(x), \qquad \left\{ \begin{array}{@{\!\!\!\!\!\!}ll} &u(t,a)=\widetilde u_a(t), \\[2pt] &u(t,b)=\widetilde u_b(t), \end{array} \right. \end{equation}} on the domain

A Singular Limit Problem for Conservation Laws Related to the Camassa–Holm Shallow Water Equation

\Omega=\{(t,x)\in\R^2:t\geq 0,\ a\le x\leq b\}

A Convergent Finite Difference Scheme for the Camassa-Holm Equation with General

. We study the mixed problem (\ref{eq:1}) from the point of view of control theory, taking the initial data

H^1

\overline u

Initial Data

fixed and regarding the boundary data

CONSERVATION LAWS WITH TIME DEPENDENT DISCONTINUOUS COEFFICIENTS

\widetilde u_a

Convergence of vanishing capillarity approximations for scalar conservation laws with discontinuous fluxes

,

Analytic Solutions and Singularity Formation for the Peakon b-Family Equations

\widetilde u_b