33 citations · 105 across the 11 of their papers we have counts for
14 papers
Global solutions for the one-dimensional Boussinesq-Peregrine system under small bottom variation
Luc Molinet, Raafat Talhouk
The Boussinesq-Peregrine system is derived from the water waves system in presence of topographic variation under the hypothesis of shallowness and small amplitude regime. The syst…
Microscopic tridomain model of electrical activity in the heart with dynamical gap junctions. Part 2 -- Derivation of the macroscopic tridomain model by unfolding homogenization method
Fakhrielddine Bader, Mostafa Bendahmane, Mazen Saad +1
We study the homogenization of a novel microscopic tridomain system, allowing for a more detailed analysis of the properties of cardiac conduction than the classical bidomain and m…
Microscopic Tridomain Model of Electrical Activity in the Heart with Dynamical Gap Junctions. Part 1 -- Modeling and Well-Posedness
Fakhrielddine Bader, Mostafa Bendahmane, Mazen Saad +1
We present a novel microscopic tridomain model describing the electrical activity in cardiac tissue with dynamical gap junctions. The microscopic tridomain system consists of three…
Three Scale Unfolding Homogenization Method Applied to Cardiac Bidomain Model
Fakhrielddine Bader, Mostafa Bendahmane, Mazen Saad +1
In this paper, we are dealing with a rigorous homogenization result at two different levels for the bidomain model of cardiac electro-physiology. The first level associated with th…
Derivation of a new macroscopic bidomain model including three scales for the electrical activity of cardiac tissue
Fakhrielddine Bader, Mostafa Bendahmane, Mazen Saad +1
In the present paper, a new three-scale asymptotic homogenization method is proposed to study the electrical behavior of the cardiac tissue structure with multiple heterogeneities…
On well-posedness for some Korteweg-De Vries type equations with variable coefficients
Luc Molinet, Raafat Talhouk, Ibtissame Zaiter
In this paper, KdV-type equations with time- and space-dependent coefficients are considered. Assuming that the dispersion coefficient in front of is positive and uniform…