Recent advances in the analysis of the dissipative Aw–Rascle system
[Avancées récentes dans l’analyse du système dissipatif Aw–Rascle]
Ewelina Zatorska1
1 Mathematics Institute, University of Warwick Zeeman Building, Coventry CV4 7AL, United Kingdom
Journées équations aux dérivées partielles (2024), Exposé no. 10, 12 p.

Le système Aw–Rascle (AR) unidimensionnel est devenu un pilier des modèles macroscopiques pour le trafic véhiculaire à une seule voie. L’une des généralisations possibles de ce modèle dans un cadre multidimensionnel est le modèle AR dissipatif, mieux adapté pour décrire la dynamique des foules. Cette revue résume les travaux récents qui analysent le modèle AR dissipatif, sa limite de congestion forte, la non-unicité des solutions faibles, l’existence et l’asymptotique des solutions dans le cadre de la dualité, les interactions non-locales et l’existence de solutions régulières.

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.

Publié le :
DOI : 10.5802/jedp.691
Classification : 35L65, 35Q31, 76N10
Keywords: Dissipative Aw–Rascle system, weak-solutions, Young measures, convex integration, duality solutions, hard congestion limit
Mot clés : Système dissipatif d’Aw–Rascle, solutions faibles, mesures de Young, intégration convexe, solutions de dualité, limite de congestion dure
Ewelina Zatorska 1

1 Mathematics Institute, University of Warwick Zeeman Building, Coventry CV4 7AL, United Kingdom 
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Ewelina Zatorska. Recent advances in the analysis of the dissipative Aw–Rascle system. Journées équations aux dérivées partielles (2024), Exposé no. 10, 12 p. doi : 10.5802/jedp.691. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.691/

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