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By studying the Riemann problem for the Aw–Rascle traffic model with different pressure laws, which is the coupling of two one-dimensional hyperbolic systems, we investigate the resonance phenomena. The main difficulty arises from the possible resonance behavior which may result in multiple solutions. We discover a new and interesting phenomenon showing that there exist infinitely many solutions for some certain initial data, which is quite different compared to earlier studies for the isentropic model of a fluid flow in a nozzle with variable cross-section and the shallow water equations with discontinuous topography. In order to overcome this difficulty, we impose the so-called TV-condition to obtain the uniqueness of solution to the Riemann problem.

The resonance behavior for the coupling of two Aw–Rascle traffic models