Memory Effects Arising in the Homogenization of Composites with Inclusions

We want to describe the asymptotic behavior, as ε-> 0,of the solution of a first order evolution problem set in a domain of Rn with periodic inclusions of size ε and prescribing a jump on the interface proportional to the conormal derivatives by means of a function of order ε^γ. The limit behaviors obtained are different according to the values of the parameter y. In particular, for y = 1, a linear memory term appears in the homogenized problem