### Approximate controllability of linear parabolic equations in perforated domains

In this paper we consider an approximate controllability problem for linear parabolic equations with rapidly oscillating coefficients in a periodically perforated domain. The holes are $\epsilon $-periodic and of size $\epsilon $. We show that, as $\epsilon \to 0$, the approximate control and the corresponding solution converge respectively to the approximate control and to the solution of the homogenized problem. In the limit problem, the approximation of the final state is alterated by a constant which depends on the proportion...