%0 Journal Article
%T Diffusion through a composite structure with a high contrasting diffusivity
%+ Université de Toulon (UTLN)
%+ Institut de Mathématiques de Marseille (I2M)
%A Sili, Ali
%< avec comité de lecture
%@ 0921-7134
%J Asymptotic Analysis
%I IOS Press
%V 89
%N 1-2
%P 173-187
%8 2014
%D 2014
%R 10.3233/ASY-141241
%K homogenization
%K high contrast
%K conductivity
%K degenerate equation
%K volume fraction
%Z Mathematics [math]/Analysis of PDEs [math.AP]Journal articles
%X We consider the stationary diffusion equation in a periodic composite medium made of two components Mε and Bε having very different diffusivity, the ratio between the coefficients of the diffusion in that structure being 1/αε2, where ε is the size of the period and αε which represents the amplitude of the diffusion in the inclusions Bε is a decreasing sequence towards zero. We show that the inclusions Bε work on the macroscopic diffusion as holes. In particular for scalings 0<αε ε corresponding to very weak diffusion in Bε, the volume fraction of the material at the limit is the well known one in the case of holes.
%G English
%L hal-01256452
%U https://hal.science/hal-01256452
%~ UNIV-TLN
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ I2M
%~ I2M-2014-
%~ TDS-MACS