N. Burq et P. Gerard, A NECESSARY AND SUFFICIENT CONDITION FOR THE EXACT CONTROLLABILITY OFTHE WAVE-EQUATION, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 325(7), 1997, pp. 749-752
We show that the geometric control condition of C. Barrios, G. Lebeau,
and J. Rauch is a necessary and sufficient condition for the exact co
ntrollability of the wave equation with Dirichlet boundary conditions.