Abstract:

In this paper, we study the Riemann problem for the Euler equations of compressible fluid flow with a composite source term. The source can cover a Coulomb-like friction or a damping or both. Different from the homogeneous system, Riemann solutions of the inhomogeneous system are non self-similar. Concentration and cavitation in the pressureless limit of solutions to the Riemann problem for the Euler equations of compressible fluid flow with a composite source term are investigated in detail as the adiabatic exponent tends to one. We rigorously proved that, as the adiabatic exponent tends to one, any two-shock Riemann solution tends to a delta shock solution of the pressureless Euler system with a composite source term, and the intermediate density between the two shocks tends to a weighted $ \delta$-mesaure which forms the delta shock; while any two-rarefaction-wave Riemann solution tends to a two-contact-discontinuity solution of the pressureless Euler system with a composite source term, whose intermediate state between the two contact discontinuities is a vacuum state.

Key words: Pressureless limit, Euler equations of compressible fluid flow, Composite source term, Delta shock wave, Vacuum state, Riemann problem