The Riemann problem with delta initial data for the non-isentropic improved Aw-Rascle-Zhang model

DOI10.1007/s10473-023-0114-7OpenAlexW4306686061MaRDI QIDQ2088160

Tong Li, Tingting Chen, Zhen Wang, Wei-Feng Jiang

Publication date: 21 October 2022

Published in: Acta Mathematica Scientia. Series B. (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10473-023-0114-7

zbMATH Keywords

Riemann problemwave interactionstraffic flow\(\delta\)-shock wavenon-isentropic improved Aw-Rascle-Zhang model

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) PDEs in connection with fluid mechanics (35Q35) Hyperbolic conservation laws (35L65) Traffic problems in operations research (90B20)

Related Items (1)

Limits of solutions to the Aw-Rascle traffic flow model with generalized Chaplygin gas by flux approximation

Cites Work

• Delta shock wave with Dirac delta function in multiple components for the system of generalized Chaplygin gas dynamics
• Developing an Aw-Rascle model of traffic flow
• Formation of delta shocks and vacuum states in the vanishing pressure limit of Riemann solutions to the perturbed Aw-Rascle model
• Existence of global bounded weak solutions to nonsymmetric systems of Keyfitz-Kranzer type
• The vanishing pressure limit of Riemann solutions to the non-isentropic Euler equations for generalized Chaplygin gas
• Solutions with concentration to the Riemann problem for the one-dimensional Chaplygin gas equations
• The rate of entropy increase at the edge of chaos
• Multidimensional shock interaction for a Chaplygin gas
• The Riemann problem with delta initial data for the one-dimensional Chaplygin gas equations with a source term
• Global solutions of nonconcave hyperbolic conservation laws with relaxation arising from traffic flow
• The Aw-Rascle traffic model with Chaplygin pressure
• The Riemann problem with delta initial data for the one-dimensional Chaplygin gas equations
• The asymptotic limits of Riemann solutions for the isentropic extended Chaplygin gas dynamic system with the vanishing pressure
• Existence and uniqueness of the global \(L^1\) solution of the Euler equations for Chaplygin gas
• Stability of the Riemann solutions for a Chaplygin gas
• Measure solutions of one-dimensional piston problem for compressible Euler equations of Chaplygin gas
• The comparison of the Riemann solutions in gas dynamics
• Delta shock wave in the compressible Euler equations for a Chaplygin gas
• The Riemann problem with delta initial data for a class of coupled hyperbolic systems of conservation laws
• A model for the formation and evolution of traffic jams
• Nonlinear dynamics of traffic jams
• On the stability of the improved Aw-Rascle-Zhang model with Chaplygin pressure
• Extensions and Amplifications of a Traffic Model of Aw and Rascle
• General limiting behavior of Riemann solutions to the non-isentropic Euler equations for modified Chaplygin gas
• Coupling Conditions for a Class of Second-Order Models for Traffic Flow
• Interactions of Elementary Waves for the Aw–Rascle Model
• The Riemann problem for the transportation equations in gas dynamics
• Congestion on Multilane Highways
• Resurrection of "Second Order" Models of Traffic Flow
• INTERACTIONS OF DELTA SHOCK WAVES FOR THE AW-RASCLE TRAFFIC MODEL WITH SPLIT DELTA FUNCTIONS
• Traffic Flow on a Road Network Using the Aw–Rascle Model
• A Hybrid Lagrangian Model Based on the Aw–Rascle Traffic Flow Model
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