2 citations · 5 across the 16 of their papers we have counts for
17 papers
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…
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…
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…
A nonlocal regularization of a generalized Busenberg-Travis cross-diffusion system
Ansgar Jüngel, Martin Vetter, Antoine Zurek
A cross-diffusion system with Lotka-Volterra reaction terms in a bounded domain with no-flux boundary conditions is analyzed. The system is a nonlocal regularization of a generaliz…
A convergent finite-volume scheme for nonlocal cross-diffusion systems for multi-species populations
Ansgar Jüngel, Stefan Portisch, Antoine Zurek
An implicit Euler finite-volume scheme for a nonlocal cross-diffusion system on the one-dimensional torus, arising in population dynamics, is proposed and analyzed. The kernels are…
Analysis of a one dimensional energy dissipating free boundary model with nonlinear boundary conditions. Existence of weak solutions
Benoît Merlet, Juliette Venel, Antoine Zurek
This work is part of a general study on the long-term safety of the geological repository of nuclear wastes. A diffusion equation with a moving free boundary in one dimension is in…
Study of an entropy dissipating finite volume scheme for a nonlocal cross-diffusion system
Maxime Herda, Antoine Zurek
In this paper we analyse a finite volume scheme for a nonlocal version of the Shigesada-Kawazaki-Teramoto (SKT) cross-diffusion system. We prove the existence of solutions to the s…
Analysis of a finite-volume scheme for a single-species biofilm model
Christoph Helmer, Ansgar Jüngel, Antoine Zurek
An implicit Euler finite-volume scheme for a parabolic reaction-diffusion system modeling biofilm growth is analyzed and implemented. The system consists of a degenerate-singular d…
A discrete boundedness-by-entropy method for finite-volume approximations of cross-diffusion systems
Ansgar Jüngel, Antoine Zurek
An implicit Euler finite-volume scheme for general cross-diffusion systems with volume-filling constraints is proposed and analyzed. The diffusion matrix may be nonsymmetric and no…
Nonlocal cross-diffusion systems for multi-species populations and networks
Ansgar Jüngel, Stefan Portisch, Antoine Zurek
Nonlocal cross-diffusion systems on the torus, arising in population dynamics and neuroscience, are analyzed. The global existence of weak solutions, the weak-strong uniqueness, an…
A convergent structure-preserving finite-volume scheme for the Shigesada-Kawasaki-Teramoto population system
Antoine Zurek, Ansgar Jüngel
An implicit Euler finite-volume scheme for an -species population cross-diffusion system of Shigesada--Kawasaki--Teramoto-type in a bounded domain with no-flux boundary conditio…
Convergence of a finite-volume scheme for a degenerate-singular cross-diffusion system for biofilms
Esther S. Daus, Ansgar Jüngel, Antoine Zurek
An implicit Euler finite-volume scheme for a cross-diffusion system modeling biofilm growth is analyzed by exploiting its formal gradient-flow structure. The numerical scheme is ba…
A finite-volume scheme for a cross-diffusion model arising from interacting many-particle population systems
Ansgar Jüngel, Antoine Zurek
A finite-volume scheme for a cross-diffusion model arising from the mean-field limit of an interacting particle system for multiple population species is studied. The existence of…