Stoker, J.J. (1957) Water Waves: The mathematical Theory with Applications. Interscience, New York.

has been cited by the following article:

• TITLE: Study of the 1D Saint-Venant Equations and Application to the Simulation of a Flood Problem

  AUTHORS: Maman Yarodji Abdoul Kader, Rabé Badé, Bisso Saley

  KEYWORDS: Shallow Water Equations, Hyperbolic System, Finite Volume Method, Weak Solution

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.8 No.7, July 8, 2020

  ABSTRACT: In this paper we are concerned with the mathematical and numerical analysis of the one-dimensional Saint-Venant equations. Thus, we prove the existence of a weak solution for any fixed time and with low regularity on the data. For the numerical approach we use the Rusanov scheme to approximate the flux and the hydrostatic reconstruction method which consists of decentering the source term at the interface. A numerical test of the proposed resolution is performed on a non-uniform topography.