# Paola Goatin

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)
• 7
• Numerische Mathematik
• 2010
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)
We consider solutions of the Aw-Rascle model for traffic flow fulfilling a constraint on the flux at x = 0. Two different kinds of solutions are proposed: at x = 0 the first one conserves both the number of vehicles and the generalized momentum, while the second one conserves only the number of cars. We study the invariant domains for these solutions and we(More)
• SIAM Journal of Applied Mathematics
• 2011
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)
• 1
• Mathematical biosciences and engineering : MBE
• 2015
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)