Existence of solutions to a boundary value problem for a phase transition traffic model

Abstract

We consider the initial boundary value problem for the phase transition traffic model introduced in [9], which is a macroscopic model based on a 2 × 2 system of conservation laws. We prove existence of solutions by means of the wave-front tracking technique, provided the initial data and the boundary conditions have finite total variation.

A Riemann solver at a junction compatible with a homogenization limit

“…The traffic model considered in this paper is a system of 2 × 2 conservation laws; it belongs to the class of macroscopic second order models as the famous Aw-Rascle-Zhang model, see [1,19]. As the name Phase Transition suggests, the model is characterized by two different phases, the free one and the congested one; see [2,4,5,7,8,10,14,16,17] and the references therein for similar descriptions. The Phase Transition model we consider here is derived from the famous Lighthill-Whitham-Richards one [15,18] by assuming that different drivers may have different maximal speeds.…”

On The Microscopic Modeling of Vehicular Traffic on General Networks

“…The former ones are usually based on partial differential equations, their prototype being the Lighthill-Whitham [27] and Richards [32] model. Deep criticisms [16] led to the formulation of entirely new continuum models, such as [2], or multiphase models [4,8,13,20,29] and models on networks, starting from [21] up to the recent monograph [18].…”