Abstract

In this article, we study the homogenization of the family of parabolic equations over periodically perforated domains a,b (x/d(e), u(epsilon)) - div a(u(epsilon), delu(epsilon)) = f(x, t) in Omega(epsilon) x (0, T), u(epsilon) = 0 on partial derivativeOmega(epsilon) x (0, T), u(epsilon) (x, 0) = u(0)(x) in Omega(epsilon). Here, Omega(epsilon) = Omega\ S-epsilon is a periodically perforated domain and d(epsilon) is a sequence of positive numbers which goes to zero. We obtain the homogenized equation. The homogenization of the equations on a fixed domain and also the case of perforated domain with Neumann boundary condition was studied by the authors. The homogenization for a fixed domain and b(x/d(epsilon), u(epsilon)) = b(u(epsilon)) has been done bit Jian. We also obtain certain corrector results to improve the weak convergence.