Interactions of Elementary Waves for the Aw–Rascle Model

Abstract

In this paper, we study the interactions of elementary waves for the traffic flow model proposed by Aw and Rascle in [SIAM J. Appl. Math., 60 (2000), pp. 916–938]. The solutions are obtained constructively when the initial data are three piecewise constant states. In particular, a new wave $SJ$ in which a shock wave S and a contact discontinuity J coincide with each other is obtained during the process of interaction. Moreover, by studying the limits of the solutions as the perturbed parameter $\varepsilon$ tends to zero, it can be found that the Riemann solutions are stable for such perturbations with the initial data.