The Riemann problem of one dimensional shallow water equations with discontinuous topography has been constructed recently. The elementary waves include shock waves, rarefaction waves, and the stationary wave. The stationary wave appears when the water depth changes, especially when there exists a bottom step. In this paper, we are mainly concerned with the interaction between a stationary wave with either a shock wave or a rarefaction wave. By using the characteristic analysis methods, the evolution of waves is described during the interaction process. The solution in large time scale is also presented in each case. The results may contribute to research on more complicated wave interaction problems.

中文翻译：

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具有不连续地形的浅水方程基本波的相互作用

最近已经构建了具有不连续地形的一维浅水方程的黎曼问题。基本波包括冲击波、稀疏波和驻波。驻波出现在水深变化时，尤其是存在底阶时。在本文中，我们主要关注驻波与激波或稀疏波之间的相互作用。利用特征分析方法，描述了相互作用过程中波的演化过程。每种情况下也都给出了大时间尺度的解决方案。该结果可能有助于研究更复杂的波相互作用问题。