Abstract

The resonant cases in the Riemann problem for a model of two-phase flows with resonance are investigated, which complete the construction of Riemann solutions. The model is given by a nonconservative hyperbolic system of balance laws. The phase decomposition method is developed to construct solutions in each phase in a relatively separated way, but still glued to each other via the contact discontinuities. Composite wave curves can be built and intersections of wave curves in each phase plane help to determine various configurations of Riemann solutions. In particular, solutions containing multiple waves propagating with the same shock speed are constructed.