A class of strictly hyperbolic systems of conservation laws are proposed and studied. Firstly, the Riemann problem with initial data of two piecewise constant states is constructively solved. The solutions involving contact discontinuities and delta shock waves are obtained. The generalized Rankine–Hugoniot relation and entropy condition for the delta shock wave are clarified and the existence and uniqueness of the delta-shock solution is proved. Furthermore, the global structure of solutions with five different configurations is constructed via investigating the interactions of delta shock waves and contact discontinuities. Finally, we present a typical example to illustrate the application of the system introduced.

中文翻译：

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一类严格守恒定律双曲系统的黎曼问题和波相互作用

提出并研究了一类严格的守恒定律双曲线系统。首先，建设性地求解了具有两个分段常数状态初始数据的黎曼问题。获得了涉及接触不连续性和增量冲击波的解决方案。阐明了δ激波的广义Rankine-Hugoniot关系和熵条件，证明了δ激波解的存在唯一性。此外，通过研究 delta 冲击波和接触不连续性的相互作用，构建了具有五种不同配置的解决方案的全局结构。最后，我们通过一个典型的例子来说明所介绍的系统的应用。