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Zbl 0957.35086
Aw, A.; Rascle, M.
Resurrection of ``second order" models of traffic flow. (English)
[J] SIAM J. Appl. Math. 60, No.3, 916-938 (2000). ISSN 0036-1399; ISSN 1095-712X/e

The authors deal with the 2nd order (two equations) mathematical model of traffic flow and point out drawbacks of currently used models. They change the model by replacing space derivation of the ``pressure'' with a convective one. The resulting system is strictly hyperbolic, except at the origin. The solution of the Riemann problem is described in details, including the case of the vacuum (i.e. the case of very low traffic). Remarks on the admissibility and stability of the solution are presented. Comparing the solution to the new proposed model with the solution to the older model shows that the older model predicts unrealistic solutions with negative velocities whereas the new model gives a correct answer.
[A.Doktor (Praha)]

MSC 2000:: *35L65 Conservation laws
90B20 Highway traffic
35L80 Hyperbolic equations of degenerate type
35Q35 Other equations arising in fluid mechanics

Keywords: traffic flow; conservation laws; Riemann problem

Cited in: Zbl 1249.35216 Zbl 1206.35169 Zbl 1185.35144 Zbl 1173.90355 Zbl 1165.90374 Zbl 1153.90356 Zbl 1136.35054 Zbl 1148.35049 Zbl 1244.90060 Zbl 1090.90032 Zbl 0994.90023

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