A Sturm-Liouville theorem is proved for quadratic operator pencils to count unstable real roots, with applications to wave stability.
Spectral stability of hydraulic shock profiles
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
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.
fields
math.CA 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
A Sturm Liouville theorem for quadratic operator pencils
A Sturm-Liouville theorem is proved for quadratic operator pencils to count unstable real roots, with applications to wave stability.