NUMERICAL CONTROL OF THE WAVE EQUATION AND HUYGENS' PRINCIPLE

The numerical control of the wave equation is investigated in dimension 2 and 3. Using Huygens' principle in dimension 3 (resp. the method of descent in dimension 2), we show that the exact controllability of the wave equation can be obtained numerically on a cuboid (resp. on a rectangle) in sharp time with a boundary control supported on adjacent sides, by directly solving the wave equation on a larger domain. As a consequence, the numerical control of the wave equation is not affected here by the appearance of high frequency spurious numerical waves, and no filtering is needed.