BOUNDARY CONTROLLABILITY FOR CONSERVATIVE PDES

Boundary observability and controllability problems for evolution equa tions governed by PDEs have been greatly studied in the past years. Ho wever, the problems were studied on a case-by-case basis, only for som e particular types of boundary controls, and, moreover, several unnatu ral restrictions concerning lower-order terms were used. Our goal here is to give a general approach for boundary controllability problems, which is valid for all evolution PDEs of hyperbolic or ultrahyperbolic type, all boundary controls for which the corresponding homogeneous p roblem is well-posed, and all well-posedness spaces for the homogeneou s problem. The first example of such equations is the class of hyperbo lic equations, but valid examples are also equations such as the Schro edinger equation and various models for the plate equation. This work is essentially based on some a priori estimates of Carleman's type obt ained by the author in a previous paper [29].