Dirichlet problem associated with a random quasilinear operator in a random domain
Dispersive limits in the homogenization of the wave equation
Effective saturation for composite porous media
This paper is devoted to the study of the homogenization of a porous medium, composed of different materials arranged in a periodic structure. This provides the profile of the saturation function for the limit material.
Error estimates on homogenization of free boundary velocities in periodic media
Estimates of eigenvalues and eigenfunctions in periodic homogenization
For a family of elliptic operators with rapidly oscillating periodic coefficients, we study the convergence rates for Dirichlet eigenvalues and bounds of the normal derivatives of Dirichlet eigenfunctions. The results rely on an estimate in for solutions with Dirichlet condition.
Étude de transmission à travers des inclusions minces faiblement conductrice de «codimension un» : homogénéisation et optimisation des structures
Exact relations for composites: Towards a complete solution.
Existence of a solution to with a maximal monotone graph in for every given
Fibered microstructures for some nonlocal Dirichlet forms
Fluides légèrement compressibles et limite incompressible
Fourier approach to homogenization problems
This article is divided into two chapters. The classical problem of homogenization of elliptic operators with periodically oscillating coefficients is revisited in the first chapter. Following a Fourier approach, we discuss some of the basic issues of the subject: main convergence theorem, Bloch approximation, estimates on second order derivatives, correctors for the medium, and so on. The second chapter is devoted to the discussion of some non-classical behaviour of vibration problems of periodic...
Fourier approach to homogenization problems
This article is divided into two chapters. The classical problem of homogenization of elliptic operators with periodically oscillating coefficients is revisited in the first chapter. Following a Fourier approach, we discuss some of the basic issues of the subject: main convergence theorem, Bloch approximation, estimates on second order derivatives, correctors for the medium, and so on. The second chapter is devoted to the discussion of some non-classical behaviour of vibration problems of periodic...
-convergence and homogenization of monotone damped hyperbolic equations.
Global-Local subadditive ergodic theorems and application to homogenization in elasticity
Ground states of singularly perturbed convection-diffusion equation with oscillating coefficients
We study the first eigenpair of a Dirichlet spectral problem for singularly perturbed convection-diffusion operators with oscillating locally periodic coefficients. It follows from the results of [A. Piatnitski and V. Rybalko, On the first eigenpair of singularly perturbed operators with oscillating coefficients. Preprint www.arxiv.org, arXiv:1206.3754] that the first eigenvalue remains bounded only if the integral curves of the so-called effective drift have a nonempty ω-limit set. Here we consider...
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.