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 $\hat{I}\mu$ - the scale of the microstructure, for the projection of solutions to the subspace generated by the eigenfunctions with eigenvalues less that $C\hat{I}{\mu }^{-1/2}$.

This revised version corrects a flaw in the proof of one of the main theorems in the previous version. The statements of the main results are revised. The previous version was published in JEMS 24, pp.3031-3053 (2022) with an erratum in the same issue