Harmonic measures of perforated domains
Homogénéisation d'équations hyperboliques du premier ordre et application aux écoulements miscibles en milieu poreux
Homogénéisation variationnelle des équations d’Euler
Homogenization and corrector for the wave equation in domains with small holes
Homogenization and diffusion asymptotics of the linear Boltzmann equation
We investigate the diffusion limit for general conservative Boltzmann equations with oscillating coefficients. Oscillations have a frequency of the same order as the inverse of the mean free path, and the coefficients may depend on both slow and fast variables. Passing to the limit, we are led to an effective drift-diffusion equation. We also describe the diffusive behaviour when the equilibrium function has a non-vanishing flux.
Homogenization and Diffusion Asymptotics of the Linear Boltzmann Equation
We investigate the diffusion limit for general conservative Boltzmann equations with oscillating coefficients. Oscillations have a frequency of the same order as the inverse of the mean free path, and the coefficients may depend on both slow and fast variables. Passing to the limit, we are led to an effective drift-diffusion equation. We also describe the diffusive behaviour when the equilibrium function has a non-vanishing flux.
Homogenization and hyperbolicity
Homogenization and localization in locally periodic transport
In this paper, we study the homogenization and localization of a spectral transport equation posed in a locally periodic heterogeneous domain. This equation models the equilibrium of particles interacting with an underlying medium in the presence of a creation mechanism such as, for instance, neutrons in nuclear reactors. The physical coefficients of the domain are -periodic functions modulated by a macroscopic variable, where is a small parameter. The mean free path of the particles is also...
Homogenization and localization in locally periodic transport
In this paper, we study the homogenization and localization of a spectral transport equation posed in a locally periodic heterogeneous domain. This equation models the equilibrium of particles interacting with an underlying medium in the presence of a creation mechanism such as, for instance, neutrons in nuclear reactors. The physical coefficients of the domain are ε-periodic functions modulated by a macroscopic variable, where ε is a small parameter. The mean free path of the particles...
Homogenization and two-scale convergence of the compressible Reynolds lubrication equation modelling the flying characteristics of a rough magnetic head over a rough rigid-disk surface
Homogenization and uniform stabilization for a nonlinear hyperbolic equation in domains with holes of small capacity.
Homogenization at different linear scales, bounded martingales and the two-scale shuffle limit
In this paper, we consider two-scale limits obtained with increasing homogenization periods, each period being an entire multiple of the previous one. We establish that, up to a measure preserving rearrangement, these two-scale limits form a martingale which is bounded: the rearranged two-scale limits themselves converge both strongly in L2 and almost everywhere when the period tends to +∞. This limit, called the Two-Scale Shuffle limit, contains all the information present in all the two-scale...
Homogenization in chemical reactive flows.
Homogenization in elastodynamics with force term depending on time.
Homogenization in perforated domains with rapidly pulsing perforations
The aim of this paper is to study a class of domains whose geometry strongly depends on time namely. More precisely, we consider parabolic equations in perforated domains with rapidly pulsing (in time) periodic perforations, with a homogeneous Neumann condition on the boundary of the holes. We study the asymptotic behavior of the solutions as the period of the holes goes to zero. Since standard conservation laws do not hold in this model, a first difficulty is to get a priori estimates of the...
Homogenization in perforated domains with rapidly pulsing perforations
The aim of this paper is to study a class of domains whose geometry strongly depends on time namely. More precisely, we consider parabolic equations in perforated domains with rapidly pulsing (in time) periodic perforations, with a homogeneous Neumann condition on the boundary of the holes. We study the asymptotic behavior of the solutions as the period ε of the holes goes to zero. Since standard conservation laws do not hold in this model, a first difficulty is to get a priori estimates...
Homogenization of a boundary condition for the heat equation
An asymptotic analysis is given for the heat equation with mixed boundary conditions rapidly oscillating between Dirichlet and Neumann type. We try to present a general framework where deterministic homogenization methods can be applied to calculate the second term in the asymptotic expansion with respect to the small parameter characterizing the oscillations.
Homogenization of a capillary phenomena.
We study the height of a liquid in a tube when it contains a great number of thin vertical bars and when its border is finely strained. For this, one uses an epi-convergence method.
Homogenization of a carcinogenesis model with different scalings with the homogenization parameter
In the context of periodic homogenization based on two-scale convergence, we homogenize a linear system of four coupled reaction-diffusion equations, two of which are defined on a manifold. The system describes the most important subprocesses modeling the carcinogenesis of a human cell caused by Benzo-[a]-pyrene molecules. These molecules are activated to carcinogens in a series of chemical reactions at the surface of the endoplasmic reticulum, which constitutes a fine structure inside the cell....
Homogenization of a dual-permeability problem in two-component media with imperfect contact
In this paper, we study the macroscopic modeling of a steady fluid flow in an -periodic medium consisting of two interacting systems: fissures and blocks, with permeabilities of different order of magnitude and with the presence of flow barrier formulation at the interfacial contact. The homogenization procedure is performed by means of the two-scale convergence technique and it is shown that the macroscopic model is a one-pressure field model in a one-phase flow homogenized medium.