Recent advances in the analysis of the dissipative Aw-Rascle system

TL;DR

This paper reviews recent advances in analyzing the dissipative Aw-Rascle system, a model for traffic and crowd dynamics, focusing on solution properties, limits, and interactions.

Contribution

It summarizes recent research on the dissipative AR model, including solution existence, limits, and non-local interactions, highlighting new mathematical insights.

Findings

Analysis of the hard congestion limit

Non-uniqueness of weak solutions

Existence and asymptotics of solutions

Abstract

The one-dimensional Aw-Rascle (AR) system has become a cornerstone of macroscopic models for single-lane vehicular traffic. A possible generalization of this model to a multi-dimensional setting is the so-called dissipative AR model, which is more suited to capturing crowd dynamics. This review summarizes recent studies that analyze the dissipative AR model, its hard congestion limit, the non-uniqueness of weak solutions, the existence and asymptotics of solutions within the duality framework, non-local interactions, and the existence of regular solutions.