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A spectral study of the boundary controllability of the linear 2-D wave equation in a rectangle

The paper studies the controllability properties of the linear 2-D wave equation in the rectangle Ω = (0, a) × (0, b). We consider two types of action, on an edge or on two adjacent edges of the boundary. Our analysis is based on Fourier expansion and explicit construction and evaluation of biorthogonal sequences. This method allows us to measure the magnitude of the control needed for each eigenfrequency. In both analyzed cases we give a Fourier characterization of the controllable spaces of initial data and we construct particular controls for them.