Boundary Observability and Controllability for Evolutions Governed by Higher Order PDE

In a recent work Bardos et al. [SIAM J. Control Optim. 30 (1992), no. 5, 1024-1065] have obtained sharp results on boundary observability and controllability for second-order hyperbolic equations. The essential idea there is that one can observe (control) the solution along any generalized bicharacteristic which hits the boundary at a nondiffractive point; this condition is called the geometric optics condition. Our goal here is to extend their results to higher order hyperbolic problems and ultrahyperbolic problems. As their work is based on Melrose-Stronsjand results on propagation of singularities [R. B. Melrose and J. Sjostrand, Comm. Pure Appl. Math. 31 (1978), 593-617; 35 (1982), 129-168], ours is based on [D. Tataru, Propagation of singularities at the boundary for higher order PDE, preprint], which extends these results to higher order hyperbolic and ultrahyperbolic equations.