Weakly singular shock profiles for a non-dispersive regularization of shallow-water equations
Résumé
We study a regularization of the classical Saint-Venant (shallow-water) equations, recently introduced by D. Clamond and D. Dutykh (Commun. Nonl. Sci. Numer. Simulat. 55 (2018) 237-247). This regularization is non-dispersive and formally conserves mass, momentum and energy. We show that for every classical shock wave, the system admits a corresponding non-oscillatory traveling wave solution which is continuous and piecewise smooth, having a weak singularity at a single point where energy is dissipated as it is for the classical shock. The system also admits cusped solitary waves of both elevation and depression.
Domaines
Mécanique des fluides [physics.class-ph] Dynamique des Fluides [physics.flu-dyn] Equations aux dérivées partielles [math.AP] Analyse classique [math.CA] Analyse numérique [math.NA] Physique Atmosphérique et Océanique [physics.ao-ph] Physique Numérique [physics.comp-ph] Formation de Structures et Solitons [nlin.PS] Systèmes Solubles et Intégrables [nlin.SI]
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