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February  2001, 1(1): 61-70. doi: 10.3934/dcdsb.2001.1.61

Non-persistence of roll-waves under viscous perturbations

Pascal Noble 1, and  Sebastien Travadel 1,

1. 

Mathématiques pour I'Industrie et la Physique, UFR MIG 118, route de Narbonne, 31062 Toulouse Cedex, France, France

Received  October 2000 Revised  January 2001 Published  January 2001

In this paper, we study the existence of periodic traveling waves for the equations of the Shallow-water theory with a small viscosity. This small viscosity leads to a singularly perturbed problem. The slow-fast system involves a point where normal hyperbolicity breaks down. We first prove the existence of a slow manifold around this point. Then we show that there are no periodic solutions for small viscosity and describe completely the structure of a travelling wave.
Keywords: roll waves, Shallow-water equations, singular perturbations..
Mathematics Subject Classification: 34C2.
Citation: Pascal Noble, Sebastien Travadel. Non-persistence of roll-waves under viscous perturbations. Discrete & Continuous Dynamical Systems - B, 2001, 1 (1) : 61-70. doi: 10.3934/dcdsb.2001.1.61
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