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 Lp, p≥2, the first complete stability results for large-amplitude shock profiles of a hyperbolic relaxation system.
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