Uniform boundary controllability and homogenization of wave equations

Abstract

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 $\epsilon$ (the scale of the microstructure) for the projection of solutions to the subspace generated by the eigenfunctions with eigenvalues less than $C{\epsilon }^{-2/3}$.

A correction to this paper is available.