Stability of Viscous St. Venant Roll Waves: From Onset to Infinite Froude Number Limit
نویسندگان
چکیده
منابع مشابه
Nonlinear Stability of Viscous Roll Waves
Extending results of Oh–Zumbrun and Johnson–Zumbrun for parabolic conservation laws, we show that spectral stability implies nonlinear stability for spatially periodic viscous roll wave solutions of the one-dimensional St. Venant equations for shallow water flow down an inclined ramp. The main new issues to be overcome are incomplete parabolicity and the nonconservative form of the equations, w...
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A technical obstruction preventing the conclusion of nonlinear stability of large-Froude number roll waves of the St. Venant equations for inclined thin film flow is the ”slope condition” of Johnson-Noble-Zumbrun, used to obtain pointwise symmetrizability of the linearized equations and thereby high-frequency resolvent bounds and a crucial H nonlinear damping estimate. Numerically, this conditi...
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The purpose of this article is to study the persistence of solution of a hyperbolic system under small viscous perturbation. Here, the solution of the hyperbolic system is supposed to be periodic: it is a periodic perturbation of a roll-wave. So, it has an infinity of shocks. The proof of the persistence is based on an expansion of the viscous solution and estimates on Green’s functions. Keywor...
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We study by a combination of numerical and analytical Evans function techniques the stability of solitary wave solutions of the St. Venant equations for viscous shallowwater flow down an incline, and related models. Our main result is to exhibit examples of metastable solitary waves for the St. Venant equations, with stable point spectrum indicating coherence of the wave profile but unstable es...
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ژورنال
عنوان ژورنال: Journal of Nonlinear Science
سال: 2016
ISSN: 0938-8974,1432-1467
DOI: 10.1007/s00332-016-9333-6