Instabilities in generic second-order traffic models with relaxation

DOI10.1007/s00033-024-02307-7MaRDI QIDQ6612979

Alessandra Rizzo, Paola Goatin

Publication date: 1 October 2024

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

zbMATH Keywords

relaxationhyperbolic systems of conservation lawsstop-and-go wavesmacroscopic traffic flow modelssub-characteristic condition

Mathematics Subject Classification ID

First-order nonlinear hyperbolic equations (35L60) Hyperbolic conservation laws (35L65) Traffic problems in operations research (90B20) Initial value problems for first-order hyperbolic systems (35L45)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Constructing set-valued fundamental diagrams from jamiton solutions in second order traffic models
• Comparative model accuracy of a data-fitted generalized Aw-Rascle-Zhang model
• The zero relaxation limit for the Aw-Rascle-Zhang traffic flow model
• \(L^ 1\) nonlinear stability of traveling waves for a hyperbolic system with relaxation
• The zero relaxation limit for the hydrodynamic Whitham traffic flow model
• The semigroup generated by a Temple class system with large data
• Viscosity solutions and uniqueness for systems of inhomogeneous balance laws
• An improved macroscopic model of traffic flow: Derivation and links with the Lighthill-Whitham model
• On the validity of Chapman-Enskog expansions for shock waves with small strength
• The BGK approximation of kinetic models for traffic
• A multiscale model for traffic regulation via autonomous vehicles
• Moving bottlenecks for the Aw-Rascle-Zhang traffic flow model
• Viscous profiles in models of collective movement with negative diffusivity
• Global Solutions and Zero Relaxation Limit for a Traffic Flow Model
• A second-order model for vehicular traffics with local point constraints on the flow
• A General Phase Transition Model for Vehicular Traffic
• Zero relaxation and dissipation limits for hyperbolic conservation laws
• Hyperbolic conservation laws with stiff relaxation terms and entropy
• Resurrection of "Second Order" Models of Traffic Flow
• Shock Waves on the Highway
• A 2-Phase Traffic Model Based on a Speed Bound
• On the Partial Difference Equations of Mathematical Physics
• On kinematic waves II. A theory of traffic flow on long crowded roads
• Macroscopic traffic flow modelling: from kinematic waves to autonomous vehicles
• The initial boundary value problem for second order traffic flow models with vacuum: existence of entropy weak solutions
• Autonomous Vehicles Driving Traffic: The Cauchy Problem

This page was built for publication: Instabilities in generic second-order traffic models with relaxation