Skip to Main content Skip to Navigation
Journal articles

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.
Document type :
Journal articles
Complete list of metadata

Cited literature [20 references]  Display  Hide  Download

https://hal.inria.fr/hal-01713987
Contributor : Paola Goatin <>
Submitted on : Wednesday, February 21, 2018 - 10:35:25 AM
Last modification on : Friday, May 21, 2021 - 1:48:14 PM
Long-term archiving on: : Tuesday, May 22, 2018 - 1:07:59 PM

File

DGR.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01713987, version 1

Citation

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

Share

Metrics

Record views

603

Files downloads

539