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AN ANALYSIS OF RIEMANN SOLUTIONS FOR THE NONHOMOGENEOUS AW–RASCLE MODEL OF TRAFFIC FLOW WITH THE BORN–INFELD EQUATION OF STATE
Part of:
Hyperbolic equations and systems
Published online by Cambridge University Press: 01 December 2025
Abstract
This paper focuses on the Aw–Rascle model of traffic flow for the Born–Infeld equation of state with Coulomb-like friction, whose Riemann problem is solved with the variable substitution method. Four kinds of nonself-similar solutions are derived. The delta shock occurs in the solutions, although the system is strictly hyperbolic with a genuinely nonlinear characteristic field and a linearly degenerate characteristic field. The generalized Rankine–Hugoniot relation and entropy condition for the delta shock are clarified. The delta shock can be used to describe the serious traffic jam. Under the impact of the friction term, the rarefaction wave (R), shock wave (S), contact discontinuity (J) and delta shock (
$\delta $) are bent into parabolic curves. Furthermore, it is proved that the 
$S+J$ solution and 
$\delta $ solution of the nonhomogeneous Aw–Rascle model tend to be the 
$\delta $ solution of the zero-pressure Euler system with friction; the 
$R+J$ solution and 
$R+\mbox {Vac}+J$ solution tend to be the vacuum solution of the zero-pressure Euler system with friction.
Keywords
MSC classification
Primary:
35L65: Conservation laws
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- Research Article
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- © The Author(s), 2025. Published by Cambridge University Press on behalf of the Australian Mathematical Publishing Association Inc
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