Macroscopic traffic models: shifting from densities to ``celerities

DOI10.1016/j.amc.2010.02.032zbMath1198.90081OpenAlexW1982468837MaRDI QIDQ603046

Jean-Pierre Aubin

Publication date: 5 November 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2010.02.032

zbMATH Keywords

congestionviabilitycapture basinsDaganzo variational principleLax-HopfLighthillMoskowitzNewelltraffic functionWhitham and Richards equation

Mathematics Subject Classification ID

Applications of optimal control and differential games (49N90) Traffic problems in operations research (90B20)

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Lax-Hopf formula and Max-Plus properties of solutions to Hamilton-Jacobi equations ⋮ Traveling waves for a microscopic model of traffic flow ⋮ Regulation of viable and optimal cohorts ⋮ Traveling wave profiles for a follow-the-leader model for traffic flow with rough road condition ⋮ Regulation of births for viability of populations governed by age-structured problems ⋮ Nonlocal multi-scale traffic flow models: analysis beyond vector spaces ⋮ Tropical Geometries and Dynamics of Biochemical Networks Application to Hybrid Cell Cycle Models ⋮ Rigorous derivation of nonlinear scalar conservation laws from follow-the-leader type models via many particle limit

Cites Work

• Unnamed Item
• Unnamed Item
• Some Properties of Viscosity Solutions of Hamilton-Jacobi Equations
• Dirichlet Problems for some Hamilton–Jacobi Equations with Inequality Constraints
• Solutions to Switched Hamilton-Jacobi Equations and Conservation Laws Using Hybrid Components
• Viability-Based Computations of Solutions to the Hamilton-Jacobi-Bellman Equation
• Viscosity Solutions of Hamilton-Jacobi Equations
• Shock Waves on the Highway
• On kinematic waves II. A theory of traffic flow on long crowded roads
• Set-valued analysis