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

In this article, we study the homogenization of the family of parabolic equations over periodically perforated domains partial derivative(t)b (x/epsilon, u(epsilon)) - diva (x/epsilon, u(epsilon), delu(epsilon)) = f(x, t) in Omega(epsilon) x (0, T), a (x/epsilon, u(epsilon), delu(epsilon)) . nu(epsilon) = 0 on partial derivativeS(epsilon) x (0, T), u(epsilon) = 0 on partial derivativeOmega x (0, T), u(epsilon) (x, 0) = u(0)(x) in Omega(epsilon). Here, Omega(epsilon) = Omega\S-epsilon is a periodically perforated domain. We obtain the homogenized 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/epsilon, u(epsilon)) = b(u(epsilon)) has been done by Jian [11].