Homogenization of a parabolic equation in perforated domain with Neumann boundary condition

Abstract

In this article, we study the homogenization of the family of parabolic equations over periodically perforated domains @tb x ;u diva x ;u; ru Df.x;t/ in  .0;T/; a x ;u; ru : D 0o n@S .0;T/; u D 0o n@.0;T/; u.x; 0/ Du0.x/ in : Here,  Dn S is a periodically perforated domain. We obtain the homoge- nized equation and corrector results. The homogenization of the equations on a fixed domain was studied by the authors (15). The homogenization for a fixed domain and b x ;u b.u/ has been done by Jian (11).