Existence of Pulsating Roll-Waves for the Saint Venant System |
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Authors: | Pascal Noble |
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Institution: | (1) Institut Camille Jordan, UMR 5208, Université Claude Bernard Lyon 1, 43 boulevard du 11 November 1918, 69622 Villeurbanne Cedex, France |
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Abstract: | The phenomenon of roll-waves occurs when shallow water flows down open inclined channels. This flow is described by the Saint
Venant’s equations with a friction term due to Chezy. In the case of a flat bottom, their existence (as entropic and periodic
travelling waves) follows from a classical work due to DRESSLER 6].
The aim of this paper is to prove the existence of roll-waves when the bottom is modulated by a small periodic perturbation.
Following JIN and KATSOULAKIS 15], we first compute a Burgers-type equation which possesses “pulsating” roll-waves (the wave
speed oscillates around an average velocity). We prove, in a mathematically rigorous fashion, the existence of these solutions. |
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