We give a comprehensive presentation of the periodic unfolding method for perforated domains, both when unit hole is compact subset open cell and this impossible to achieve. In order apply boundary-value problems with nonhomogeneous Neumann conditions on boundaries holes, properties boundary operator are also extensively studied. The paper concludes applications such examples reiterated unfolding.

We consider the Neumann problem in a domain with periodic holes. The size of basic cell and holes is order ε. Some homogenization theorems are proved. There essentially two limit cases as ε→0. In first one mean value t

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In this paper we describe the asymptotic behavior of a problem depending on small parameter ε>0 and modelling stationary heat diffusion in two-component conductor. The flow is proportional to jump temperature field, due contact resistance interface. More precisely, give an homogenization result for equation with oscillating coefficients domain [Formula: see text] ℝ n , where connected union ε-periodic disconnected inclusions size ε. These two sub-domains Ω are separated by surface Γ ε...

In this paper, we apply the periodic unfolding method in perforated domains introduced by Cioranescu et al. (Portugal. Math. 63(4) (2006), 467–496) to a class of elliptic problems with nonlinear conditions on boundary holes. A new compactness result will play major role homogenization process and provides correctors without using any extension operator.

We study the Stokes system with non-homogeneous Fourier boundary conditions depending on a parameter, in domain periodic inclusions of size period. Following values this we obtain at limit Darcy's law, Brinkmann type equation or equation. also present physical model to which results apply. This describes flow an incompressible viscous fluid through porous medium under action exterior electric field.

Abstract This article is devoted to the homogenization of a quasilinear elliptic equation with oscillating coefficients in periodically perforated domain. A nonlinear Robin condition prescribed on boundary holes, depending real parameter γ ≥ 1. We suppose that data satisfy some suitable hypotheses which ensure, as proved by authors Cabarrubias and Donato [B. P. Donato, Existence uniqueness for problem conditions, Carpathian J. Math. (2) (2011) (to appear)], existence solution problem. In...

The paper deals with existence and homogenization for elliptic problems lower order terms singular in the u-variable (u is solution) a cylinder $Q$ $\mathbb{R}^N$, so that term becomes infinite on set $\{u=0\}$. A rapidly oscillating interface inside separates two composite connected components. has periodic microstructure it situated small neighborhood of hyperplane which components $Q$. At we suppose following transmission conditions: (i) flux continuous, (ii) jump solution at proportional...

The aim of this paper is to provide the correctors associated homogenization a parabolic problem describing heat transfer. results here complete earlier study in [Jose, Rev. Roumaine Math. Pures Appl. 54 (2009) 189–222] on asymptotic behaviour domain with two components separated by an ε-periodic interface. physical model established [Carslaw and Jaeger, Clarendon Press, Oxford (1947)] prescribes interface condition that flux temperature proportional jump field, factor order εγ. We suppose...

We present here some corrector results for the homogenization of wave equation in a two-component composite with $\varepsilon$-periodic connected inclusions which complete proved [P. Donato, L. Faella, and S. Monsurrò, J. Math. Pures Appl., 87 (2007), pp. 119–143] by authors. On interface separating two components we prescribe jump solution proportional to conormal derivatives via function order $\varepsilon^\gamma$, $-1<\gamma\leq1$. Due different expressions energies limit problems, cases...

This paper deals with an existence and uniqueness result of a weak solution for quasilinear elliptic boundary value problem in domain whose is the union two disjoint closed surfaces. On interior we prescribe nonlinear Robin condition suitable growth assumptions, on exterior boundary, Dirichlet condition. The main difficulty when proving due to condition, since, order apply fixed point theorem, need prove continuity associated operator. To this aim, first study several properties

In this paper we give a general presentation of the homogenization Neumann type problems in periodically perforated domains, including case where shape reference hole varies with size period (in spirit construction self-similar fractals). We shows that H0-convergence holds under extra assumption there exists bounded sequence extension operators for holes. The class Jones-domains gives an example result applies. When fails, another approach, using Poincaré–Wirtinger inequality is presented. A...

The paper deals with homogenization of an elliptic boundary valueproblem stated in a domain which consists two connected components separatedby rapidly oscillating interface periodic microstructure, theinterface being situated small neighbourhood hyperplane. At we suppose the following transmission conditions: (i) flux is continuous,(ii) jump solution at proportional to fluxthrough interface. &nbsp; &nbspWe derive homogenized problem and effective conditionfor different values ratio between...