Asymptotic behavior of Riemann solutions for the inhomogeneous Aw-Rascle-Zhang traffic model with the logarithmic equation of state

Abstract

The exact Riemann solutions are solved constructively for the inhomogeneous Aw-Rascle-Zhang traffic model with the logarithmic equation of state under the Coulomb-like friction term, where all the emerged waves are bent into the parabola curves with the same curvature grade under the influence of this friction term. On the one side, the 1-shock front tends to the stationary 2-contact discontinuity front and eventually coincides to form a curved delta shock front when the traffic pressure vanishes, where the accompanied concentration phenomenon can be observed and explored. On the other side, the head of the 1-rarefaction wave tends to the stationary 2-contact discontinuity front as well as the tail of the 1-rarefaction wave is changed into the 1-contact discontinuity front when the traffic pressure vanishes, where the associated cavitation phenomenon can also be inspected and discussed.