“ 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 epsilon-periodic imperfect inclusions. We prescibe, on the interface separating the two components, a jump of the solution proportional to the conormal derivatives via a function of order epsilon ^ gamma. For different values of gamma, we obtain different limit problems. In particular, for gamma=1, we have a linear memory term in the homogenized equation.