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Weakly singular shock profiles for a non-dispersive regularization of shallow-water equations
- Source :
- Communications in Mathematical Sciences (2018), Vol. 16, Number 5, pp. 1361-1378
- Publication Year :
- 2018
-
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.<br />Comment: 25 pages, 4 figures, 23 references. Accepted to Comm. Math. Sci. Other author's papers can be downloaded at http://www.denys-dutykh.com/
Details
- Database :
- arXiv
- Journal :
- Communications in Mathematical Sciences (2018), Vol. 16, Number 5, pp. 1361-1378
- Publication Type :
- Report
- Accession number :
- edsarx.1805.06842
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.4310/CMS.2018.v16.n5.a9