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

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.