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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
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- Journal:
- The ANZIAM Journal / Volume 67 / 2025
- Published online by Cambridge University Press:
- 01 December 2025, e39
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- Article
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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.
