The exact Riemann solutions to the generalized Chaplygin gas equations with friction

Abstract

The exact solutions to the Riemann problem for the one-dimensional generalized Chaplygin gas equations with a Coulomb-like friction term are constructed explicitly. The delta shock wave arises in the Riemann solutions provided that the initial data satisfy some certain conditions, although the system is strictly hyperbolic and the two characteristic fields are genuinely nonlinear. The position, strength and propagation speed of delta shock wave are obtained from the generalized Rankine–Hugoniot conditions. It is shown that the Coulomb-like friction term make waves (including rarefaction, shock and delta shock) bend into parabolic shapes for the Riemann solutions.