Homogenization of the wave equation in composites with imperfect interface: A memory effect

In this paper we study the asymptotic behaviour of the wave equation with rapidly oscillating coefficients in a two-component composite with ε-periodic imperfect inclusions. We prescribe on the interface between the two components a jump of the solution proportional to the conormal derivatives through a function of order ε^γ. For the different values of γ, we obtain different limit problems. In particular, for γ=1 we have a linear memory effect in the homogenized problem