Abstract
The goal of this paper is to present some homogenization results for diffusion problems in composite structures, formed by two media with different features. Our setting is relevant for modeling heat diffusion in composite materials with imperfect interfaces or electrical conduction in biological tissues. The approach we follow is based on the periodic unfolding method, which allows us to deal with general media.
Highlights
AND SETTING OF THE PROBLEMThe analysis of diffusion phenomena in highly heterogeneous materials has been a subject of huge interest in the last decades
The purpose of this paper is to analyze the effective behavior of the solution of some nonlinear problems arising in the modeling of diffusion in a periodic structure formed by two media with different properties, separated by an active interface
Our setting is relevant for modeling heat conduction in composite materials with imperfect interfaces or electrical conduction in biological tissues
Summary
The analysis of diffusion phenomena in highly heterogeneous materials has been a subject of huge interest in the last decades. We consider the case in which Ω is a periodic structure formed by two components, Ωε and Πε, representing two materials with different features, separated by an interface Sε. We assume that both Ωε and Πε = Ω \ Ωε are connected, but only Ωε reaches the external fixed boundary of the domain Ω. We can avoid the use of extension operators Using this general method, we can deal with media with less regularity than those usually considered in the literature (composite materials and biological tissues are highly heterogeneous and their interfaces are not very smooth, in general). The last section is devoted to the proof of our result
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