Homogenization of an evolution problem with LlogL data in a domain with oscillating boundary

We consider a N-dimensional structure, N∈ N { 1 } , with a very rough boundary. Precisely, in 3D the structure consists in a box with the upper side covered with ε-periodically distributed asperities having fixed height and size depending on ε. In this structure, we study the asymptotic behavior, as ε vanishes, of an evolution Neumann problem with source term and initial data having LlogL a priori estimates. We identify the limit problem.