7 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…
Constructive existence proofs and stability of stationary solutions to parabolic PDEs using Gegenbauer polynomials
Maxime Breden, Matthieu Cadiot, Antoine Zurek
In this paper, we present a computer-assisted framework for constructive proofs of existence for stationary solutions to one-dimensional parabolic PDEs and the rigorous determinati…
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…
A finite volume scheme for the local sensing chemotaxis model
Maxime Herda, Ariane Trescases, Antoine Zurek
In this paper we design, analyze and simulate a finite volume scheme for a cross-diffusion system which models chemotaxis with local sensing. This system has the same Lyapunov func…
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…