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 prescribe on the interface between the two components a jump of the solution proportional to the conormal derivatives through a function of order epsilon(gamma). For the different values of gamma, we obtain different limit problems. In particular, for gamma = 1 we have a linear memory effect in the homogenized problem. (C) 2006 Elsevier Masson SAS. All rights reserved.