3 papers
math.NA2026
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…
math.NA2026
Convergence of a scheme for a two dimensional nonlocal system of transport equations
Diana Al Zareef, Ahmad El Hajj, Antoine Zurek
In this paper, we numerically study a two-dimensional system modeling the dynamics of dislocation densities. This system is hyperbolic, but not strictly hyperbolic, and couples two…
math.NA2025
Convergence of a semi-explicit scheme for a one dimensional periodic nonlocal eikonal equation modeling dislocation dynamics
Diana Al Zareef, Ahmad El Hajj, Hassan Ibrahim +1
In this paper, we derive a periodic model from a one dimensional nonlocal eikonal equation set on the full space modeling dislocation dynamics. Thanks to a gradient entropy estimat…