Boundary observability and controllability for evolutions governed by higher order PDE (Q1900380)

This paper extends the results of C. Bardos, G. Lebeau and R. Rauch on the geometric boundary controllability of the wave equation. The results presented concern strictly hyperbolic operators and boundary conditions satisfying a weak Lopatinski condition as well as operators with anisotropic principal part in the sense that the highest order of the time derivative may be less than the maximal order of the space derivatives. They apply to the Euler-Bernoulli plate model, Schrödinger's equation and linearized KdV equation. This paper uses the anisotropic definition of the cotangent bundle, wave front set and Sobolev spaces as well as the anisotropic pseudodifferential operators. The proofs rely on previous results of the author on propagation of singularities in this framework.