2 citations · 5 across the 16 of their papers we have counts for
5 papers · 1 filter
Discrete Sobolev and Trudinger inequalities on polyhedral meshes
Maxime Herda, Ariane Trescases, Antoine Zurek
We revisit the derivation of discrete Sobolev and related inequalities on bounded domains for piecewise constant functions on polyhedral meshes. Our results improve the dependence…
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…