Comptes Rendus
On a closure of mass conservation equation and stability analysis in the mathematical theory of vehicular traffic flow
Comptes Rendus. Mécanique, Volume 332 (2004) no. 8, pp. 585-590.

This Note deals with the development of mathematical methods for the closure of the mass conservation equation for macroscopic hydrodynamical models of traffic flow on roads. The closure is obtained by a phenomenological model, relating the local mean velocity to local density earlier in time. An evolution equation is obtained for the flux and a stability analysis is performed; this qualitatively describes some features of congested flow.

Cette Note est dédiée au dévelopement d'une méthodes mathématiques pour la fermeture des équations macroscopiques de la conservation de la masse, intervenant dans la modélisation du trafic des véhicules. La fermeture est obtenue en utilisant un modèle phénoménologique approprié pour relier la vitesse moyenne locale à la densité locale (avec retard en temp). Une équation pour le flux est derivée et une analyse de stabilité est conduite.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2004.03.016
Keywords: Continuum mechanics, Traffic flow, Continuum models, Nonlinear sciences
Mot clés : Milieux continus, Flux du traffic, Models continues, Sciences non-linéaires

Vincenzo Coscia 1

1 Dipartimento di Matematica, Università di Ferrara, Via Machiavelli 35, 44100 Ferrara, Italy
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Vincenzo Coscia. On a closure of mass conservation equation and stability analysis in the mathematical theory of vehicular traffic flow. Comptes Rendus. Mécanique, Volume 332 (2004) no. 8, pp. 585-590. doi : 10.1016/j.crme.2004.03.016. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.03.016/

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