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A traffic flow model describing the formation and dynamics of traffic jams was introduced by Berthelin et al., which consists of a constrained pressureless gas dynamics system and can be derived from the Aw-Rascle model under the constraint condition ρ ρ * by letting the traffic pressure vanish. In this paper, we give up this constraint condition and consider the following formThe formal limit of the above system is the pressureless gas dynamics system in which the density develops delta-measure concentration in the Riemann solution. However, the propagation speed and the strength of the delta shock wave in the limit situation are different from the classical results of the pressureless gas dynamics system with the same Riemann initial data. In order to solve it, the perturbed Aw-Rascle model is proposed as✩ This work is partially supported by 3025 whose behavior is different from that of the Aw-Rascle model. It is proved that the limits of the Riemann solutions of the perturbed Aw-Rascle model are exactly those of the pressureless gas dynamics model.

Abstract. The Riemann problem for the changed form of the chromatography system is considered here. It can be shown that the delta shock wave appears in the Riemann solution for exactly specified initial states. The generalized Rankine-Hugoniot relation of the delta shock wave is derived in detail. The existence and uniqueness of solutions involving the delta shock wave for the Riemann problem is proven by employing the self-similar viscosity vanishing approach.