Paola Goatin

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We introduce a new model of vehicular traffic flow with phase transitions. The model is obtained by coupling together the classical Lighthill–Whitham–Richards equation with the 2× 2 system proposed by Aw and Rascle. This allows us both to correct some drawbacks of the original 2× 2 system, and to obtain results that fit experimental data well. We describe(More)
This paper is devoted to the numerical analysis of the road traffic model proposed by Colombo and Goatin in [CG07]. The model involves a standard conservation law supplemented by a local unilateral constraint on the flux at the point x = 0 (modelling a road light, a toll gate, etc.). We first show that the problem can be interpreted in terms of the theory(More)
A new version of Godunov scheme is proposed in order to compute solutions of a traffic flow model with phase transitions. The scheme is based on a modified averaging strategy and a sampling procedure. Several numerical tests are shown to prove the validity of the method. The convergence of the algorithm is demonstrated numerically. We also give a higher(More)
We solve the Riemann problem for a class of resonant hyperbolic systems of balance laws. The systems are not strictly hyperbolic and the solutions take their values in a neighborhood of a state where two characteristic speeds coincide. Our construction generalizes the ones given earlier by Isaacson and Temple for scalar equations and for conservative(More)
An extension of the Colombo phase transition model is proposed. The congestion phase is described by a two-dimensional zone defined around an equilibrium flux known as the classical fundamental diagram. General criteria to build such a set-valued fundamental diagram are enumerated, and instantiated on several equilibrium fluxes with different concavity(More)
We study invariance and viability properties of a closed set for the trajectories of either a controlled diiusion process or a controlled deterministic system with disturbances. We use the value functions associated to suitable optimal control problems or diierential games and analyze the related Dynamic Programming equation within the theory of viscosity(More)
In this article, we present a simplified model to describe the dynamics of two groups of pedestrians moving in opposite directions in a corridor. The model consists of a 2 x 2 system of conservation laws of mixed hyperbolic-elliptic type. We study the basic properties of the system to understand why and how bounded oscillations in numerical simulations(More)
We study general 2nd order fully nonlinear degenerate elliptic equations on an arbitrary closed set with generalized Dirichlet boundary conditions in the viscosity sense. We prove some properties of the maximal subsolution and the minimal supersolution of the Dirichlet type problem. Under a sort of compatibility condition on the boundary data we show that(More)