Uniform Boundary Controllability and Homogenization of Wave Equations

We obtain sharp convergence rates, using Dirichlet correctors, for solutions of wave equations in a bounded domain with rapidly oscillating periodic coefficients. The results are used to prove the exact boundary controllability that is uniform in $\e$ - the scale of the microstructure, for the projection of solutions to the subspace generated by the eigenfunctions with eigenvalues less that $C\e^{-2/3}$.