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Journal Articles Journal of Mathematical Analysis and Applications Year : 2018

Existence of BV solutions for a non-conservative constrained Aw-Rascle-Zhang model for vehicular traffic

Abstract

In this paper we study the Aw-Rascle-Zhang (ARZ) model with non-conservative local point constraint on the density flux introduce in [Garavello, M., and Goatin, P. The Aw-Rascle traffic model with locally constrained flow. Journal of Mathematical Analysis and Applications 378, 2 (2011), 634-648], its motivation being, for instance, the modeling of traffic across a toll gate. We prove the existence of weak solutions under assumptions that result to be more general than those required in [Garavello, M., and Villa, S. The Cauchy problem for the Aw-Rascle-Zhang traffic model with locally constrained flow. Journal of Hyperbolic Differential Equations 14, 03 (2017), 393-414]. More precisely, we do not require that the waves of the first characteristic family have strictly negative speeds of propagation. The result is achieved by showing the convergence of a sequence of approximate solutions constructed via the wave-front tracking algorithm. The case of solutions attaining values at the vacuum is considered. We also present an explicit numerical example to describe some qualitative features of the solutions.
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Dates and versions

hal-01713987 , version 1 (21-02-2018)

Identifiers

  • HAL Id : hal-01713987 , version 1

Cite

Nikodem S Dymski, Paola Goatin, Massimiliano D. Rosini. Existence of BV solutions for a non-conservative constrained Aw-Rascle-Zhang model for vehicular traffic. Journal of Mathematical Analysis and Applications, 2018, 467, pp.45-66. ⟨hal-01713987⟩
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