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

Michel Mehrenberger (1, 2)

1 CALVI - Scientific computation and visualization
2 IRMA - Institut de Recherche Mathématique Avancée

The boundary observability of the wave equation has been studied by many authors. A method of choice is to use the multiplier method. Recently, 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 to explicit time and constants. However, we do not reach the optimal time which can be obtained for this problem by the multiplier method.

Mots clés: Ingham inequality; Boundary exact observability; Fourier series; Wave equation

Domaines: Optimisation et contrôle [math.OC]

Michel Mehrenberger. An Ingham type proof for the boundary observability of a N-d wave equation. Comptes Rendus. Mathématique, 2009, ⟨10.1016/j.crma.2008.11.002⟩. ⟨hal-00311730⟩