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arXiv · 1810.01490

Spectral stability of hydraulic shock profiles

Alim Sukhtayev·Zhao Yang·Kevin Zumbrun
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Abstract

By reduction to a generalized Sturm Liouville problem, we establish spectral stability of hydraulic shock profiles of the Saint-Venant equations for inclined shallow-water flow, over the full parameter range of their existence, for both smooth-type profiles and discontinuous-type profiles containing subshocks. Together with work of Mascia-Zumbrun and Yang-Zumbrun, this yields linear and nonlinear $H^2\cap L^1 \to H^2$ stability with sharp rates of decay in $L^p$, $p\geq 2$, the first complete stability results for large-amplitude shock profiles of a hyperbolic relaxation system.

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Alim Sukhtayev, Zhao Yang, Kevin Zumbrun. 2018-10-02. Spectral stability of hydraulic shock profiles. https://arxiv.org/abs/1810.01490

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