BCAM Seminar Analysis of the HUM Control Operator and Exact Controllability for Semilinear Waves in Uniform Time

In this talk, we present the results of a recent joint work with G.Lebeau. We proceed to a detailed analysis of the HUM optimal control operator of J.L.Lions associated to interior control of linear waves. More precisely, under the Geometric Control Condition of Bardos-Lebeau-Rauch, we prove that this operator is an isomorphism on each Sobolev space and essentially acts individually on each frequency block of the data to be controlled. Moreover, on a compact manifold without boundary, it is an elliptic pseudo-di°Ëerential operator of zero order. We use this analysis together with Strichartz estimates to get results on the exact controllabilty for subcritical nonlinear waves in a bounded domain of R3.