Particle approximation of a constrained model for traffic flow

DOI10.1007/s00030-017-0480-8zbMath1380.35122OpenAlexW2610415859MaRDI QIDQ1688736

Florent Berthelin, Paola Goatin

Publication date: 11 January 2018

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00030-017-0480-8

zbMATH Keywords

many-particle systemconservation laws with density constraintconstrained pressureless gas dynamicsmicro-macro limit

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Theoretical approximation in context of PDEs (35A35) Traffic problems in operations research (90B20) Unilateral problems for hyperbolic systems and systems of variational inequalities with hyperbolic operators (35L87)

Related Items (4)

Hard-congestion limit of the p-system in the BV setting ⋮ Existence result for a two-dimensional system of conservation laws with unilateral constraints ⋮ Convergence of the follow-the-leader scheme for scalar conservation laws with space dependent flux ⋮ Partially congested propagation fronts in one-dimensional Navier-Stokes equations

Cites Work

• Many particle approximation of the Aw-Rascle-Zhang second order model for vehicular traffic
• On the micro-macro limit in traffic flow
• A traffic flow model with non-smooth metric interaction: well-posedness and micro-macro limit
• Deterministic particle approximation of the Hughes model in one space dimension
• The continuum limit of follow-the-leader models -- a short proof
• Deterministic particle approximation of scalar conservation laws
• A model for the evolution of traffic jams in multi-lane
• Rigorous derivation of nonlinear scalar conservation laws from follow-the-leader type models via many particle limit
• A model for the formation and evolution of traffic jams
• Derivation of Continuum Traffic Flow Models from Microscopic Follow-the-Leader Models
• EXISTENCE AND WEAK STABILITY FOR A PRESSURELESS MODEL WITH UNILATERAL CONSTRAINT
• Resurrection of "Second Order" Models of Traffic Flow
• A 2-Phase Traffic Model Based on a Speed Bound

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