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.

中文翻译：

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两相流模型的共振情况和黎曼问题

摘要 研究了共振两相流模型在黎曼问题中的共振情况，完成了黎曼解的构造。该模型由平衡定律的非保守双曲线系统给出。相分解方法被开发为以相对分离的方式在每个相中构建解决方案，但仍然通过接触不连续性相互粘合。可以构建复合波形曲线，并且每个相平面中波形曲线的交点有助于确定黎曼解的各种配置。特别是，构建了包含以相同冲击速度传播的多个波的解决方案。