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Congestion redux. (English) Zbl 1053.35087
Summary: We analyze a class of second-order traffic models and show that these models support stable oscillatory traveling waves typical of the waves observed on a congested roadway. The basic model has trivial or constant solutions where cars are uniformly spaced and travel at a constant equilibrium velocity that is determined by the car spacing. The stable traveling waves arise because there is an interval of car spacing for which the constant solutions are unstable. These waves consist of a smooth part where both the velocity and spacing between successive cars are increasing functions of a Lagrange mass index. These smooth portions are separated by shock waves that travel at computable negative velocity.
MSC:
35L60Nonlinear first-order hyperbolic equations
35L65Conservation laws
90B20Traffic problems