Abstract: We introduce a new model of traffic flow with phase transitions. The model is obtained by coupling together the classical Lighthill–Whitham–Richards (LWR) equation with the 2×2 system described in [A. Aw and M. Rascle, Resurrection of “second order” models of traffic flow, SIAM J. Appl. Math., 60 (2000), pp. 916–938. doi:10.1137/S0036139997332099]. We describe the solutions of the Riemann problem, and we compare the results with the ones obtained using the LWR model and the biphasic model described in [R.M. Colombo, Hyperbolic phase transitions in traffic flow, SIAM J. Appl. Math., 63 (2002), pp. 708–721. doi:10.1137/S0036139901393184].
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