Properties of the Wave Curves in the Shallow Water Equations with Discontinuous Topography

We first establish the monotonicity of the curves of composite waves for shallow water equations with discontinuous topography. Second, a critical investigation of the Riemann problem yields deterministic results for large data on the existence of Riemann solutions made of Lax shocks, rarefaction waves, and admissible stationary contacts. Although multiple solutions can be constructed for certain Riemann data, we can determine relatively large neighborhoods of Riemann data in which the Riemann problem admits a unique solution.