The Riemann solution to the Chaplygin pressure Aw-Rascle model with Coulomb-like friction and its vanishing pressure limit

Abstract: The Riemann solution to the Chaplygin pressure Aw-Rascle model with Coulomb-like friction is constructed explicitly and its vanishing pressure limit is analyzed precisely. It is shown that the delta shock wave appears in the Riemann solutions in some certain situations. The generalized Rankine-Hugoniot conditions of the delta shock wave are established and the exact position, propagation speed and strength of the delta shock wave are given explicitly, which enables us to see the influence of the Coulomb-like friction on the Riemann solution to the Chaplygin pressure Aw-Rascle model clearly. It is shown that the Coulomb-like friction term makes contact discontinuities and delta shock waves bend into parabolic shapes and the Riemann solutions are not self-similar anymore. Finally, the occurrence mechanism on the phenomenon of concentration and cavitation and the formation of delta shock wave and vacuum in the process of vanishing pressure limit are analyzed and identified in detail. Moreover, we show the Riemann solutions to the nonhomogeneous Chaplygin pressure Aw-Rascle model converge to the Riemann solutions to the transportation equations with the same source term as the pressure vanishes. These two results generalize those obtained in [7,38] for homogeneous equations to nonhomogeneous equations and are also applicable to the nonsymmetric system of Keyfitz-Kranzer type with the same Chaplygin pressure and Coulomb-like friction.