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The Riemann solution to the Chaplygin pressure Aw-Rascle model withCoulomb-like friction is constructed explicitly and its vanishing pressurelimit is analyzed precisely. It is shown that the delta shock wave appears inthe Riemann solutions in some certain situations. The generalizedRankine-Hugoniot conditions of the delta shock wave are established and theexact position, propagation speed and strength of the delta shock wave aregiven explicitly, which enables us to see the influence of the Coulomb-likefriction on the Riemann solution to the Chaplygin pressure Aw-Rascle modelclearly. It is shown that the Coulomb-like friction term makes contactdiscontinuities and delta shock waves bend into parabolic shapes and theRiemann solutions are not self-similar anymore. Finally, the occurrencemechanism on the phenomenon of concentration and cavitation and the formationof delta shock wave and vacuum in the process of vanishing pressure limit areanalyzed and identified in detail. Moreover, we show the Riemann solutions tothe nonhomogeneous Chaplygin pressure Aw-Rascle model converge to the Riemannsolutions to the transportation equations with the same source term as thepressure vanishes. These two results generalize those obtained in [7,38] forhomogeneous equations to nonhomogeneous equations and are also applicable tothe nonsymmetric system of Keyfitz-Kranzer type with the same Chaplyginpressure and Coulomb-like friction.

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