Biccari U. Internal control for non-local Schrödinger and wave equations involving the fractional Laplace operator, ESAIM: Control Optimization and Calculus of Variations, DOI: To appear
Abstract: We analyze the interior controllability problem for a nonlocal Schr\”odinger equation involving the fractional Laplace operator , , on a bounded domain . The controllability from a neighborhood of the boundary of the domain is obtained for exponents in the interval , while for the equation is shown to be not controllable. As a consequence of that, we obtain the controllability for a nonlocal wave equation involving the higher order fractional Laplace operator , . The results follow applying the multiplier method, joint with a Pohozaev-type identity for the fractional Laplacian, and from an explicit computation of the spectrum of the operator in the one-dimensional case.