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Abstract
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 ) distributed in an
-periodic network. Using the periodic unfolding method, when
and
go to 0 we determine the asymptotic behavior of the solution of an evolution problem.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1 We will see in Lemma 4.2 the reason of this assumption.
2 Recall that the space is the completion of
for the norm
. The Sobolev imbedding theorem implies that for
, it is a subspace of
, where
is the Sobolev exponent associated to 2. Therefore, all its elements admit 0 as limit at
of
(in the weak sense of
).