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math.AP2023
Existence and stability of nonmonotone hydraulic shocks for the Saint Venant equations of inclined thin-film flow
Grégory Faye, L. Miguel Rodrigues, Zhao Yang +1
Extending work of Yang-Zumbrun for the hydrodynamically stable case of Froude number F < 2, we categorize completely the existence and convective stability of hydraulic shock profi…
math.AP2023
Linear asymptotic stability of small-amplitude periodic waves of the generalized Korteweg--de Vries equations
Corentin Audiard, L. Miguel Rodrigues, Changzhen Sun
In this note, we extend the detailed study of the linearized dynamics obtained for cnoidal waves of the Korteweg--de Vries equation in \cite{JFA-R} to small-amplitude periodic trav…