7 papers
Analysis of a degenerate parabolic system for cell dynamics in intestinal crypts
Ahmad El Hajj, Mohamad El Hajj Chehade, Antoine Zurek
In this work, we study a system of degenerate parabolic equations modeling the dynamics of multiple cell populations in intestinal crypts. The model describes cell division, differ…
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…
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…
Diagonal hyperbolic systems with large and monotone data Part I: Global continuous solutions
Ahmad El Hajj, Régis Monneau
In this paper, we study diagonal hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution, for la…
Short time existence and uniqueness in Hölder spaces for the 2D dynamics of dislocation densities
Ahmad El Hajj
In this paper, we study the model of Groma and Balogh describing the dynamics of dislocation densities. This is a two-dimensional model where the dislocation densities satisfy a sy…
Derivation and study of dynamical models of dislocation densities
Ahmad El Hajj, H. Ibrahim, Régis Monneau
In this paper, starting from the microscopic dynamics of isolated dislocations, we explain how to derive formally mean field models for the dynamics of dislocation densities. Essen…