An Ingham type proof for the boundary observability of a N − d wave equation

Source abstract

The boundary observability of the wave equation has been studied by many authors. A method of choice is to use the multiplier method (cf. Komornik (1994)). Recently, in Ramdani et al. (2005), a first Fourier based proof is given in the case where the domain is a square, thanks to a new Hautus type test. We give here a new self-contained proof with an Ingham type approach in the more general case where the domain is a product of intervals; this leads, in contrary to the proof in Ramdani et al., to explicit time and constants. However, we do not reach the optimal time which can be obtained for this problem by the multiplier method.