32 citations · 55 across the 7 of their papers we have counts for
5 papers · 1 filter
A Splitting Method for Deep Water with Bathymetry
Afaf Bouharguane, Benjamin Melinand
In this paper we derive and prove the wellposedness of a deep water model that generalizes the Saut-Xu system for nonflat bottoms. Then, we present a new numerical method based on…
Global-in-time existence of perturbations around travelling-waves
Afaf Bouharguane
We investigate a fractional diffusion/anti-diffusion equation proposed by Andrew C. Fowler to describe the dynamics of sand dunes sheared by a fluid flow. In this paper, we prove t…
Finite difference approximations for a fractional diffusion/anti-diffusion equation
Pascal Azerad, Afaf Bouharguane
A class of finite difference schemes for solving a fractional anti-diffusive equation, recently proposed by Andrew C. Fowler to describe the dynamics of dunes, is considered. Their…
On the instability of a nonlocal conservation law
Afaf Bouharguane
We are interested in a nonlocal conservation law which describes the morphodynamics of sand dunes sheared by a fluid flow, recently proposed by Andrew C. Fowler. We prove that cons…
Simultaneous denoising and enhancement of signals by a fractal conservation law
Pascal Azerad, Afaf Bouharguane, Jean-François Crouzet
In this paper, a new filtering method is presented for simultaneous noise reduction and enhancement of signals using a fractal scalar conservation law which is simply the forward h…