Analysis of the generalised Aw-Rascle model

TL;DR

This paper extends the Aw-Rascle traffic model to multiple dimensions, proving the existence of global solutions and their consistency with classical solutions under certain conditions.

Contribution

It introduces a multi-dimensional generalization of the Aw-Rasque model and establishes the existence and uniqueness of measure-valued solutions.

Findings

Global-in-time measure-valued solutions exist for the generalized model.

Measure-valued solutions coincide with classical solutions when they exist.

The model applies to arbitrary large initial data in periodic domains.

Abstract

We consider the multi-dimensional generalization of the Aw-Rascle system for vehicular traffic. For an arbitrary large class of initial data and the periodic domain, we prove the existence of global-in-time measure-valued solutions. Moreover, using the relative energy technique, we show that the measure-valued solutions coincide with the classical solutions as long as the latter exist.