Su alcune questioni di Calcolo delle Variazioni: omogeneizzazione in domini perforati con condizioni di Neumann e rilassamento
Su alcune questioni di omogeneizzazione: formule di rappresentazione, domini perforati, funzionali non limitati
Suboptimal boundary controls for elliptic equation in critically perforated domain
Sur quelques problèmes d’homogénéisation non locale et de fluides en milieu poreux : une contribution de Abdelhamid Ziani
Dans cet article nous présentons quelques problèmes et résultats d’homogénéisation non locale pour certaines équations de type dégénéré. Nous considérons des équations de transport, une équation des ondes dégénérée et une équation différentielle de Riccati, et nous décrivons dans chacun des cas les effets non locaux induits par homogénéisation. Nous donnons aussi quelques résultats sur l’analyse mathématique des équations des fluides miscibles en milieu poreux.
Tail estimates for homogenization theorems in random media
Consider a random environment in given by i.i.d. conductances. In this work, we obtain tail estimates for the fluctuations about the mean for the following characteristics of the environment: the effective conductance between opposite faces of a cube, the diffusion matrices of periodized environments and the spectral gap of the random walk in a finite cube.
The averaging principle in the case of the Cauchy problem for quasilinear parabolic equations with variable principal part.
The boundary behavior of a composite material
In this paper, we study how solutions to elliptic problems with periodically oscillating coefficients behave in the neighborhood of the boundary of a domain. We extend the results known for flat boundaries to domains with curved boundaries in the case of a layered medium. This is done by generalizing the notion of boundary layer and by defining boundary correctors which lead to an approximation of order in the energy norm.
The boundary behavior of a composite material
In this paper, we study how solutions to elliptic problems with periodically oscillating coefficients behave in the neighborhood of the boundary of a domain. We extend the results known for flat boundaries to domains with curved boundaries in the case of a layered medium. This is done by generalizing the notion of boundary layer and by defining boundary correctors which lead to an approximation of order ε in the energy norm.
The Maxwell equation in a periodic medium : homogenization of the energy density
The method of Rothe and two-scale convergence in nonlinear problems
Modelling of macroscopic behaviour of materials, consisting of several layers or components, cannot avoid their microstructural properties. This article demonstrates how the method of Rothe, described in the book of K. Rektorys The Method of Discretization in Time, together with the two-scale homogenization technique can be applied to the existence and convergence analysis of some strongly nonlinear time-dependent problems of this type.
The -Laplacian in domains with small random holes
{ll -div (|Duh|p-2 Duh)=g, & in D Eh uhH1,p0(D Eh). . where and are random subsets of a bounded open set of . By...
The periodic unfolding method for a class of parabolic problems with imperfect interfaces
In this paper, we use the adapted periodic unfolding method to study the homogenization and corrector problems for the parabolic problem in a two-component composite with ε-periodic connected inclusions. The condition imposed on the interface is that the jump of the solution is proportional to the conormal derivative via a function of order εγ with γ ≤ −1. We give the homogenization results which include those obtained by Jose in [Rev. Roum. Math. Pures Appl. 54 (2009) 189–222]. We also get the...
The periodic unfolding method in perforated domains.
The Vlasov equation with strong mangnetic field and oscillating electric field as a model for isotop resonant separation.
The warping, the torsion and the Neumann problems in a quasi-periodically perforated domain
Time averaging for random nonlinear abstract parabolic equations.
Towards a two-scale calculus
We define and characterize weak and strong two-scale convergence in Lp, C0 and other spaces via a transformation of variable, extending Nguetseng's definition. We derive several properties, including weak and strong two-scale compactness; in particular we prove two-scale versions of theorems of Ascoli-Arzelà, Chacon, Riesz, and Vitali. We then approximate two-scale derivatives, and define two-scale convergence in spaces of either weakly or strongly differentiable functions. We also derive...
Transport dans les milieux composites fortement contrastés : le modèle du billard
Two problems in homogenization of porous media.
The main goal of this work is to present two different problems arising in Fluid Dynamics of perforated domains or porous media. The first problem concerns the compressible flow of an ideal gas through a porous media and our goal is the mathematical derivation of Darcy's law. This is relevant in oil reservoirs, agriculture, soil infiltration, etc. The second problem deals with the incompressible flow of a fluid reacting with the exterior of many packed solid particles. This is related with absorption...
Two-dimensional models of fabrics