EXISTENCE OF SOLUTIONS FOR THE AW–RASCLE TRAFFIC FLOW MODEL WITH VACUUM

DOI10.1142/S0219891608001428zbMath1185.35144MaRDI QIDQ3520555

Harald Hanche-Olsen, Marte Godvik

Publication date: 26 August 2008

Published in: Journal of Hyperbolic Differential Equations (Search for Journal in Brave)

zbMATH Keywords

non-strictly hyperbolic systemTemple system

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Hyperbolic conservation laws (35L65) Traffic problems in operations research (90B20) Initial value problems for first-order hyperbolic systems (35L45) Degenerate hyperbolic equations (35L80)

Related Items (23)

Entropy solutions for a traffic model with phase transitions ⋮ Riemann problems and wave interactions for a non-symmetric Keyfitz–Kranzer system with a source term ⋮ Solutions of the Aw-Rascle-Zhang system with point constraints ⋮ On the Cauchy problem for Aw-Rascle system with linear damping ⋮ Many particle approximation of the Aw-Rascle-Zhang second order model for vehicular traffic ⋮ Existence of global entropy solutions to general system of Keyfitz-Kranzer type ⋮ The Cauchy problem for the Aw–Rascle–Zhang traffic model with locally constrained flow ⋮ Limits of solutions to the Aw-Rascle traffic flow model with generalized Chaplygin gas by flux approximation ⋮ Heterogeneous traffic flow modelling using second-order macroscopic continuum model ⋮ 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 ⋮ A random sampling method for a family of temple-class systems of conservation laws ⋮ Riemann problems for the nonhomogeneous Aw-Rascle model ⋮ The Cauchy problem for multiphase first-contact miscible models with viscous fingering ⋮ Concentration of mass in the vanishing adiabatic exponent limit of Aw-Rascle traffic model with relaxation ⋮ Free-congested and micro-macro descriptions of traffic flow ⋮ String stability in traffic flows ⋮ Existence of global bounded weak solutions to nonsymmetric systems of Keyfitz-Kranzer type ⋮ Global entropy solutions for systems modelling polymer flooding in enhanced oil recovery ⋮ Riemann problems and exact solutions to a traffic flow model ⋮ Developing an Aw-Rascle model of traffic flow ⋮ A second-order model for vehicular traffics with local point constraints on the flow ⋮ Two-dimensional Aw-Rascle model with Chaplygin pressures: Riemann solutions consisting of contact discontinuities

Cites Work

• Unnamed Item
• Equivalence of the Euler and Lagrangian equations of gas dynamics for weak solutions
• An improved macroscopic model of traffic flow: Derivation and links with the Lighthill-Whitham model
• The Aw-Rascle vehicular traffic flow model with phase transitions
• Extensions and Amplifications of a Traffic Model of Aw and Rascle
• Derivation of Continuum Traffic Flow Models from Microscopic Follow-the-Leader Models
• Coupling Conditions for a Class of Second-Order Models for Traffic Flow
• A Multiclass Homogenized Hyperbolic Model of Traffic Flow
• ON A CLASS OF HYPERBOLIC BALANCE LAWS
• Congestion Redux
• Resurrection of "Second Order" Models of Traffic Flow
• Traffic Flow on a Road Network Using the Aw–Rascle Model
• On the Fundamental Diagram of Traffic Flow
• Solutions in the large for nonlinear hyperbolic systems of equations

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