The Riemann problem for the Suliciu relaxation system with the double-coefficient Coulomb-like friction terms

Abstract

We solve the Riemann problem for the Suliciu relaxation system with the Coulomb-like friction terms containing two constant friction coefficients. The exact Riemann solutions involving delta shock waves and contact discontinuities are obtained constructively. Via deriving the generalized Rankine–Hugoniot relations of delta shock waves in detail, all of the position, propagation speed and strength of the delta shock wave are given concretely under a suitable entropy condition. Based on this, we clearly analyze the influence of the Coulomb-like friction terms on the Riemann solutions of the Suliciu relaxation system.