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

TL;DR

This paper analyzes Riemann solutions for nonsymmetric Keyfitz-Kranzer and pressureless systems with time-dependent Coulomb-like friction, identifying contact discontinuities and delta-shocks, and showing convergence as pressure vanishes.

Contribution

It introduces generalized Rankine-Hugoniot conditions for delta-shocks in these systems with time-dependent friction, and proves solution convergence as pressure approaches zero.

Findings

Identified contact discontinuities and delta-shocks in the systems.

Derived generalized Rankine-Hugoniot conditions for delta-shocks.

Proved convergence of solutions from the Keyfitz-Kranzer system to the pressureless system.

Abstract

In this paper, we study the Riemann solutions for two systems: the nonsymmetric Keyfitz-Kranzer system and the pressureless system, both of which have a time-dependent Coulomb-like friction term. Our analysis identified two types of Riemann solutions: contact discontinuities and delta-shock solutions. We obtain generalized Rankine-Hugoniot conditions, which is the support for constructing 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, with both systems incorporating a time-dependent Coulomb-like friction term.