Contrôlabilité exacte interne dans des domaines perforés avec une condition aux limites de Fourier sur le bord des trous

Abstract

We consider the internal controllability of a generalized wave equation in a periodically perforated domain, with a Fourier type boundary condition on the boundary of the holes. First, we establish by the Hilbert uniqueness method, HUM, introduced by J.L. Lions, the existence of an exact control; afterwards, we prove that the sequence of controls weakly converges to a function which is the exact control of the homogenized system. We also prove a strong convergence result for the sequence of controls.