Formation of delta shocks and vacuum states in the vanishing pressure limit of Riemann solutions to the perturbed Aw-Rascle model

DOI10.1016/j.jde.2010.09.004zbMath1211.35193OpenAlexW2059151952MaRDI QIDQ615964

Chun Shen, Mei-na Sun

Publication date: 7 January 2011

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

Full work available at URL: https://doi.org/10.1016/j.jde.2010.09.004

zbMATH Keywords

Riemann problemdelta shock wavepressureless gas dynamics

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Singular perturbations in context of PDEs (35B25) Hyperbolic conservation laws (35L65) Traffic problems in operations research (90B20)

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Cites Work

• Unnamed Item
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• On the vacuum state for the isentropic gas dynamics equations
• Kinetic formulation of the isentropic gas dynamics and \(p\)-systems
• Delta-shock waves as limits of vanishing viscosity for hyperbolic systems of conservation laws
• On the 2-D Riemann problem for the compressible Euler equations I: Interaction of shocks and rarefaction waves
• On the \(2\)-D Riemann problem for the compressible Euler equations. II: Interaction of contact discontinuities
• A class of nonlinear, nonhyperbolic systems of conservation laws with well-posed initial value problems
• Dynamics of propagation and interaction of \(\delta\)-shock waves in conservation law systems
• Concentration and cavitation in the vanishing pressure limit of solutions to the Euler equations for nonisentropic fluids
• Spaces of weighted measures for conservation laws with singular shock solutions
• Definition and weak stability of nonconservative products
• Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics
• Riemann problems for a class of coupled hyperbolic systems of conservation laws
• A model for the formation and evolution of traffic jams
• \(\delta ^{\prime }\)-shock waves as a new type of solutions to systems of conservation laws
• 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 TRAFFIC-FLOW MODEL WITH CONSTRAINTS FOR THE MODELING OF TRAFFIC JAMS
• $ \delta$- and $ \delta'$-shock wave types of singular solutions of systems of conservation laws and transport and concentration processes
• Interactions of Elementary Waves for the Aw–Rascle Model
• Measure solutions to a strictly hyperbolic system of conservation laws
• Existence theory for nonlinear hyperbolic systems in nonconservative form
• The Riemann problem for the transportation equations in gas dynamics
• Sticky Particles and Scalar Conservation Laws
• Congestion on Multilane Highways
• Formation of $\delta$-Shocks and Vacuum States in the Vanishing Pressure Limit of Solutions to the Euler Equations for Isentropic Fluids
• Weak Solution to Pressureless Type System
• Resurrection of "Second Order" Models of Traffic Flow
• Systems of Conservation Laws with Invariant Submanifolds
• Traffic Flow on a Road Network Using the Aw–Rascle Model
• A Hybrid Lagrangian Model Based on the Aw–Rascle Traffic Flow Model
• DELTA SHOCK WAVES AS A LIMIT OF SHOCK WAVES
• Note on the compressible Euler equations with zero temperature
• Well posedness for pressureless flow

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