Entropy solutions for a two-phase transition model for vehicular traffic with metastable phase and time depending point constraint on the density flow
type: Item
instance of: scholarly article
title: Entropy solutions for a two-phase transition model for vehicular traffic with metastable phase and time depending point constraint on the density flow
zbMATH Open document ID: 1467.35219
author: Boris Andreianov
author: Carlotta Donadello
author: Massimiliano D. Rosini
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 2021-06-01T00:00:00Z
review text: This paper deals with a macroscopic two-phase transition model for vehicular traffic flow subject to a point constraint on the density flux. The two phases correspond to light and heavy traffic. Their dynamics are described respectively by the Lighthill-Whitham-Richards model \[ \rho_t+(\rho v(\rho))_x=0 \] and the Aw-Rascle-Zhang model \[ \rho_t+(\rho v(\rho, u))_x=0,\qquad (\rho W(u))_t+(\rho W(u) v(\rho, u))_x=0. \] The authors assume that the metastable phase is non empty. They explore the discrete in time point constraint mechanism, inducing flux limitation at bottlenecks. They introduce a new definition of admissible solutions for the Cauchy problem, for which they prove existence and provide a characterization. These admissible solutions attain the maximal flux allowed by the constraint whenever it is enforced, which guarantees compatibility of the constructed solutions with the modeling assumption imposed at the level of the Riemann solver.
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 90B20
Mathematics Subject Classification ID: 35L45
zbMATH DE Number: 7353419
zbMATH Keywords: phase transitions
zbMATH Keywords: Lighthill-Whitham-Richards model
zbMATH Keywords: Aw-Rascle-Zhang model
zbMATH Keywords: point constraint on the density flux
zbMATH Keywords: wave-front tracking
zbMATH Keywords: entropy conditions
reviewed by: Giuseppe Maria Coclite
MaRDI profile type: Publication
full work available at URL: s00030-021-00689-5
OpenAlex ID: W3046232754
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DOI: 10.1007/S00030-021-00689-5
description: scientific article; zbMATH DE number 7353419