Journal Articles Communications in Mathematical Sciences Year : 2018

Weakly singular shock profiles for a non-dispersive regularization of shallow-water equations

Abstract

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.
Fichier principal
Vignette du fichier
YP-RLP-DD-DC-rSV-2018.pdf (349) Télécharger le fichier
Origin Files produced by the author(s)
Loading...

Dates and versions

hal-01794005 , version 1 (17-05-2018)

Licence

Identifiers

Cite

Yue Pu, Robert L Pego, Denys Dutykh, Didier Clamond. Weakly singular shock profiles for a non-dispersive regularization of shallow-water equations. Communications in Mathematical Sciences, 2018, 16 (5), pp.1361-1378. ⟨10.4310/CMS.2018.v16.n5.a9⟩. ⟨hal-01794005⟩
389 View
228 Download

Altmetric

Share

More