In this paper we consider an approximate controllability problem for linear parabolic equations with rapidly oscillating coefficientsin a periodically perforateddomain. The holes are ε-periodic and of sizeε. Weshow that, as ε → 0, the approximate control andthe corresponding solution converge respectively to theapproximate control and to the solution of the homogenizedproblem. In the limit problem, theapproximation of the final state is alterated by a constant whichdependson theproportion of material in the perforated domain and is equal to1 whenthere are noholes. We also prove that the solution of the approximatecontrollability problem in the perforated domain behaves, as ε → 0, as that of the problem posed in the perforated domain having as rigth-hand side the (fixed) control of the limit problem.
