40 citations · 92 across the 20 of their papers we have counts for
10 papers · 1 filter
A functional inequalities approach for the field-road diffusion model with (symmetric) nonlinear exchanges
Matthieu Alfaro, Claire Chainais-Hillairet, Flore Nabet
In this note, we consider the so-called field-road diffusion model in a bounded domain, consisting of two parabolic PDEs posed on sets of different dimensions and coupled through (…
Existence of solutions and uniform bounds for the stationary semiconductor equations with generation and ionic carriers
Dilara Abdel, Alain Blaustein, Claire Chainais-Hillairet +2
We consider a stationary drift-diffusion system with ionic charge carriers and external generation of electron and hole charge carriers. This system arises, among other application…
Cross-diffusion systems coupled via a moving interface
Clément Cancès, Jean Cauvin-Vila, Claire Chainais-Hillairet +1
We propose and study a one-dimensional model which consists of two cross-diffusion systems coupled via a moving interface. The motivation stems from the modelling of complex diffus…
Long time behavior of the field-road diffusion model: an entropy method and a finite volume scheme
Matthieu Alfaro, Claire Chainais-Hillairet
We consider the so-called field-road diffusion model in a bounded domain, consisting of two parabolic PDEs posed on sets of different dimensions (a {\it field} and a {\it road} in…
Mathematical analysis of a thermodynamically consistent reduced model for iron corrosion
Clément Cancès, Claire Chainais-Hillairet, Benoît Merlet +2
We are interested in a reduced model for corrosion of iron, in which ferric cations and electrons evolve in a fixed oxide layer subject to a self-consistent electrostatic potential…
Large-time behavior of a family of finite volume schemes for boundary-driven convection-diffusion equations
Claire Chainais-Hillairet, Maxime Herda
We are interested in the large-time behavior of solutions to finite volume discretizations of convection-diffusion equations or systems endowed with non-homogeneous Dirichlet and N…
Large time behavior of a two phase extension of the porous medium equation
Ahmed Ait Hammou Oulhaj, Clément Cancès, Claire Chainais-Hillairet +1
We study the large time behavior of the solutions to a two phase extension of the porous medium equation, which models the so-called seawater intrusion problem. The goal is to iden…
Numerical analysis of a nonlinear free-energy diminishing Discrete Duality Finite Volume scheme for convection diffusion equations
Clément Cancès, Claire Chainais-Hillairet, Stella Krell
We propose a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions of drift diffusion equations. The scheme is built to preserve at the discrete level even o…
Convergence of a Finite Volume Scheme for a Corrosion Model
Claire Chainais-Hillairet, Pierre-Louis Colin, Ingrid Lacroix-Violet
In this paper, we study the numerical approximation of a system of partial dif-ferential equations describing the corrosion of an iron based alloy in a nuclear waste repository. In…
On the existence of solutions for a drift-diffusion system arising in corrosion modelling
Ingrid Lacroix-Violet, Claire Chainais-Hillairet
In this paper, we consider a drift-diffusion system describing the corrosion of an iron based alloy in a nuclear waste repository. In comparison with the classical drift-diffusion…