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December 2007 The Riemann problem for the shallow water equations with discontinuous topography
Philippe G. LeFloch, Mai Duc Thanh
Commun. Math. Sci. 5(4): 865-885 (December 2007).

Abstract

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.

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Philippe G. LeFloch. Mai Duc Thanh. "The Riemann problem for the shallow water equations with discontinuous topography." Commun. Math. Sci. 5 (4) 865 - 885, December 2007.

Information

Published: December 2007
First available in Project Euclid: 3 January 2008

zbMATH: 1145.35082
MathSciNet: MR2375051

Subjects:
Primary: 35L65 , 76L05 , 76N10

Keywords: conservation law , discontinuous topography , Riemann problem , shallow water

Rights: Copyright © 2007 International Press of Boston

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Vol.5 • No. 4 • December 2007
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