Communications in Mathematical Sciences
Volume 5 (2007)
The Riemann problem for the shallow water equations with discontinuous topography
Pages: 865 – 885
We construct the solution of the Riemann problem for the shallow water equations with discontinuous topography. The system under consideration is non-strictly hyperbolic and does not admit a fully conservative form, and we establish the existence of two-parameter wave sets, rather than wave curves. The selection of admissible waves is particularly challenging. Our construction is fully explicit, and leads to formulas that can be implemented numerically for the approximation of the general initial-value problem.
shallow water; conservation law; Riemann problem; discontinuous topography
2010 Mathematics Subject Classification
35L65, 76L05, 76N10