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

Yue Pu, Robert L. Pego, Denys Dutykh, Didier Clamond

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

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., 55:237-247, 2018]. 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.

Original languageBritish English
Pages (from-to)1361-1378
Number of pages18
JournalCommunications in Mathematical Sciences
Volume16
Issue number5
DOIs
StatePublished - 2018

Keywords

  • Cuspons
  • Energy loss
  • Green-Naghdi equations
  • Long waves
  • Peakons
  • Serre equations
  • Shallow water
  • Weak solutions

Fingerprint

Dive into the research topics of 'Weakly singular shock profiles for a non-dispersive regularization of shallow-water equations'. Together they form a unique fingerprint.

Cite this