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.
Key words Chaplygin gas equations, Riemann problem, delta shock wave, Coulomb-like friction term.
MSC (2010) 35L65, 35L67, 35B30, 76N10The Riemann solutions for the one-dimensional Chaplygin gas equations with a Coulomb-like friction term are constructed explicitly. It is shown that the delta shock wave appears in the Riemann solutions in some certain situations. The generalized Rankine-Hugoniot conditions of delta shock wave are established and the position, propagation speed and strength of delta shock wave are given, which enables us to see the influence of Coulomb-like friction term on the Riemann solutions for the Chaplygin gas equations clearly. In addition, the relations connected with the area transportation are derived which include mass and momentum transportation.
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