Optimal control for a second order linear evolution problem in a domain with oscillating boundary

This paper is concerned with the study of homogenization of an optimal controlproblem governed by a second-order linear evolution equation with ahomogeneous Neumann boundary condition in a domain bounded at the bottom by asmooth wall and at the top by a rough wall. The latter is assumed to consistin a plane wall covered with periodically distributed asperities, with a fixed height, whose sizedepends on a small parameter epsilon. Weidentify the limit problem and we remark that both limit state equation andlimit cost are different from those ones at epsilon level.