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Feppon, Florian

We derive high order homogenized models for the incompressible Stokes system in a cubic domain filled with periodic obstacles. These models have the potential to unify the three classical limit problems (namely the ``unchanged' Stokes system, the Brinkman model, and the Darcy's law) corresponding to various asymptotic regimes of the ratio $\eta\equ...

Feppon, Florian Jing, Wenjia

This article is a sequel to our previous work [13] concerned with the derivation of high-order homogenized models for the Stokes equation in a periodic porous medium. We provide an improved asymptotic analysis of the coefficients of the higher order models in the low-volume fraction regime whereby the periodic obstacles are rescaled by a factor $\e...

Feppon, Florian

We derive high order homogenized models for the Poisson problem in a cubic domain periodically perforated with holes where Dirichlet boundary conditions are applied. These models unify the three possible kinds of limit problems derived by the literature for various asymptotic regimes (namely the "unchanged" Poisson equation, the Poisson problem wit...

MURAT, Francois Sili, Ali

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Giachetti, Daniela Martinez-Aparicio, Pedro J. Murat, François

In the present paper we perform the homogenization of the semilinear elliptic problem: ---------- u^ε ≥ 0 in Ω^ε, ---------- - div A(x) Du^ε = F(x, u^ε) in Ω^ε, ---------- u^ε= 0 on ∂Ω^ε. ---------- In this problem F(x, s) is a Carathéodory function such that 0 ≤ F(x, s) ≤ h(x) / Γ(s) a.e. x in Ω for every s > 0, with h in some L^r(Ω) and Γ a C^1([...

Griso, Georges Merzougui, Louiza

The aim of this paper is to study the homogenization of a diffusion process which takes place in a binary structure made by an ambient connected phase surrounding the suspensions (very small particles of diameter of order εδ) distributed in an ε-periodic network. Using the periodic unfolding method introduced in [4], in the critical case, when ε an...