29 citations · 51 across the 4 of their papers we have counts for
4 papers
Convergence of a scheme for a one dimensional nonlocal and nonlinear eikonal equation
Diana Al Zareef, Ahmad El Hajj, Antoine Zurek
In this work, we study a one-dimensional nonlocal and nonlinear eikonal equation without sign restriction on its spatial gradient. The equation is characterized by weak regularity…
Homogenization of dislocation dynamics
A. El Hajj, H. Ibrahim, R. Monneau
In this paper we consider the dynamics of dislocations with the same Burgers vector, contained in the same glide plane, and moving in a material with periodic obstacles. We study t…
Dislocation dynamics: from microscopic models to macroscopic crystal plasticity
A. El Hajj, H. Ibrahim, R. Monneau
In this paper we study the connection between four models describing dislocation dynamics: a generalized 2D Frenkel-Kontorova model at the atomic level, the Peierls-Nabarro model,…
Global existence for a system of non-linear and non-local transport equations describing the dynamics of dislocation densities
Marco Cannone, Ahmad El Hajj, Regis Monneau +1
In this paper, we study the global in time existence problem for the Groma-Balogh model describing the dynamics of dislocation densities. This model is a two-dimensional model wher…