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

Michel Mehrenberger 1, 2
1 CALVI - Scientific computation and visualization
IRMA - Institut de Recherche Mathématique Avancée, LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection, Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine
Abstract : 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.
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Submitted on : Wednesday, August 20, 2008 - 3:42:50 PM
Last modification on : Friday, November 26, 2021 - 6:00:09 PM
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Michel Mehrenberger. An Ingham type proof for the boundary observability of a N-d wave equation. Comptes Rendus. Mathématique, Académie des sciences (Paris), 2009, ⟨10.1016/j.crma.2008.11.002⟩. ⟨hal-00311730⟩



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