Existence and Computation of Solutions of a Model of Traffic Involving Hysteresis

DOI10.1137/19M1269567zbMath1454.35235MaRDI QIDQ5139095

Haitao Fan, Chi-Wang Shu

Publication date: 7 December 2020

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

zbMATH Keywords

hysteresisdiscontinuous coefficientsweak solutionsporous mediaBorel measureLagrangian coordinatestraffic flowtotal variation diminishingtwo phase flownonconservative hyperbolic systemstop-and-gophantom jam

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Traffic problems in operations research (90B20) Applications to the sciences (65Z05) Weak solutions to PDEs (35D30) Applications of queueing theory (congestion, allocation, storage, traffic, etc.) (60K30) First-order hyperbolic systems (35L40) Hysteresis for ordinary differential equations (34C55) Traveling wave solutions (35C07)

Related Items

String stability in traffic flows, High order numerical methods for flows with hysteretic fluxes

Cites Work

• Unnamed Item
• High resolution schemes for hyperbolic conservation laws
• Definition and weak stability of nonconservative products
• Two-phase flow in porous media with hysteresis
• Godunov method for nonconservative hyperbolic systems
• Why Nonconservative Schemes Converge to Wrong Solutions: Error Analysis
• Representation of Weak Limits and Definition of Nonconservative Products
• Shock Waves on the Highway
• Numerical methods for nonconservative hyperbolic systems: a theoretical framework.
• On kinematic waves II. A theory of traffic flow on long crowded roads
• Modeling hysteresis in porous media flow via relaxation