Riemann problem for a nonsymmetric Keyfitz–Kranzer and pressureless gas systems with a time-dependent Coulomb-like friction term

Abstract

In this paper, we study the Riemann solutions for two systems: the nonsymmetric Keyfitz–Kranzer system and the pressureless system, both characterized by a time-dependent Coulomb-like friction term. Our analysis identifies two types of Riemann solutions: contact discontinuities and delta-shock solutions. We obtain generalized Rankine–Hugoniot conditions, which support the construction of the delta-shock solution for the nonsymmetric Keyfitz–Kranzer system with a time-dependent Coulomb-like friction term. Furthermore, we demonstrate that as the pressure tends to zero, the Riemann solutions of the nonsymmetric Keyfitz–Kranzer system converge to those of the pressureless system, both incorporating a time-dependent Coulomb-like friction term.