Well-Posedness for Scalar Conservation Laws with Moving Flux Constraints

DOI10.1137/18M1172211zbMath1437.35491arXiv1801.04814OpenAlexW2784111943WikidataQ114847162 ScholiaQ114847162MaRDI QIDQ4631719

Benedetto Piccoli, Thibault Liard

Publication date: 18 April 2019

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.04814

zbMATH Keywords

traffic flow modelingtangent vectorswavefront trackingscalar conservation laws with constraintsbackwards in time method

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Traffic problems in operations research (90B20) Initial value problems for first-order hyperbolic equations (35L03)

Related Items (7)

A multiscale model for traffic regulation via autonomous vehicles ⋮ Control of multi-agent systems: results, open problems, and applications ⋮ Macroscopic traffic flow modelling: from kinematic waves to autonomous vehicles ⋮ A PDE-ODE model for traffic control with autonomous vehicles ⋮ Interacting moving bottlenecks in traffic flow ⋮ A Macroscopic Traffic Flow Model Accounting for Bounded Acceleration ⋮ Influence of a slow moving vehicle on traffic: well-posedness and approximation for a mildly nonlocal model

Cites Work

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• Special issue on mathematics of traffic flow modeling, estimation and control
• On the multiscale modeling of vehicular traffic: from kinetic to hydrodynamics
• Conservation laws on complex networks
• Scalar conservation laws with moving constraints arising in traffic flow modeling: an existence result
• Convergent and conservative schemes for nonclassical solutions based on kinetic relations. I
• A contractive metric for systems of conservation laws with coinciding shock and rarefaction curves
• A conservative scheme for non-classical solutions to a strongly coupled PDE-ODE problem
• Feedback control algorithms for the dissipation of traffic waves with autonomous vehicles
• Flows on networks: recent results and perspectives
• Stability estimates for scalar conservation laws with moving flux constraints
• Moving bottlenecks for the Aw-Rascle-Zhang traffic flow model
• A front tracking method for a strongly coupled PDE-ODE system with moving density constraints in traffic flow
• Polygonal approximations of solutions of the initial value problem for a conservation law
• Moving Bottlenecks in Car Traffic Flow: A PDE-ODE Coupled Model
• Modeling of moving bottlenecks in traffic flow: a PDE-ODE model with moving density constraints
• A Traffic Model for Velocity Data Assimilation
• A Tracking Algorithm for Car Paths on Road Networks
• Uniqueness for discontinuous ODE and conservation laws
• A Hölder continuous ODE related to traffic flow
• Well-posedness of the Cauchy problem for 𝑛×𝑛 systems of conservation laws
• Resurrection of "Second Order" Models of Traffic Flow
• Shock Waves on the Highway
• On kinematic waves II. A theory of traffic flow on long crowded roads
• Front tracking for hyperbolic conservation laws

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