Spectral stability of hydraulic shock profiles

2018/10/02 by Sukhtayev, Alim, Yang, Zhao, Zumbrun, Kevin
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.01490

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 H²∩ L¹ → H² stability with sharp rates of decay in L^p, p≥ 2, the first complete stability results for large-amplitude shock profiles of a hyperbolic relaxation system.

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