Abstract We investigate the Riemann Problem for a shallow water model with porosity and terrain data. Based on recent results on the local existence, we build the solution in the large settings (the magnitude of the jump in the initial data is not supposed to be “small enough”). One di culty for the extended solution arises from the double degeneracy of the hyperbolic system describing the model. Another di culty is given by the fact that the construction of the solution assumes solving an equation which has no global solution. Finally, we present some cases to illustrate the existence and non-existence of the solution.

中文翻译：

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带地形和植被的浅水方程黎曼问题解的构造方法

摘要 我们研究了具有孔隙度和地形数据的浅水模型的黎曼问题。基于最近关于局部存在的结果，我们在大设置中构建解决方案（初始数据中的跳跃幅度不应该“足够小”）。扩展解的一个困难来自描述模型的双曲线系统的双重退化。另一个难点在于，解的构造假设求解一个没有全局解的方程。最后，我们通过一些案例来说明解的存在和不存在。