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A second-order model for vehicular traffics with local point constraints on the flow

Boris Andreianov

Laboratoire de Mathématiques, Université de Franche-Comté, 16 Route de Gray, Besançon Cedex, 25030, France

E-mail Address: boris.andreianov@univ-fcomte.fr

Current affiliation: LMPT, CNRS UMR 7350, Université de Tours, Parc de Grandmont 37200 Tours, France.

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Carlotta Donadello

Laboratoire de Mathématiques, Université de Franche-Comté, 16 Route de Gray, Besançon Cedex, 25030, France

E-mail Address: carlotta.donadello@univ-fcomte.fr

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Massimiliano Daniele Rosini

Instytut Matematyki, Uniwersytet Marii Curie-Skłodowskiej, Pl. Marii Curie-Skłodowskiej 1, 20-031, Lublin, Poland

E-mail Address: mrosini@umcs.lublin.pl

Corresponding author

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https://doi.org/10.1142/S0218202516500172Cited by:29 (Source: Crossref)

Abstract

In this paper we present a second-order model based on the Aw, Rascle, Zhang model (ARZ) for vehicular traffics subject to point constraints on the flow, its motivation being, for instance, the modeling of traffic lights along a road. We first introduce a definition of entropy solution by choosing a family of entropy pairs analogous to the Kruzhkov entropy pairs for scalar conservation laws; then we apply the wave-front tracking method to prove existence and a priori bounds for the entropy solutions of constrained Cauchy problem for ARZ with initial data of bounded variation and piecewise constant constraints. The case of solutions attaining values at the vacuum is considered. We construct an explicit example to describe some qualitative features of the solutions.

Communicated by K. Zumbrun

Keywords:

AMSC: 35L65, 90B20

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