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An Ingham type proof for a two-grid observability theorem

Paola Loreti 1 Michel Mehrenberger 2, 3
2 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 : Here, we prove the uniform observability of a two-grid method for the semi-discretization of the 1D-wave equation for a time $t>2\sqrt{2}$; this time, if the observation is made in $(-T/2,T/2)$, is optimal and this result improves an earlier work of Negreanu and Zuazua [C. R. Acad. Sci. Paris Sér. I 338 (2004) 413–418]. Our proof follows an Ingham type approach.
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Submitted on : Wednesday, April 6, 2016 - 8:56:29 PM
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Paola Loreti, Michel Mehrenberger. An Ingham type proof for a two-grid observability theorem. ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2008, ⟨10.1051/cocv:2007062⟩. ⟨hal-01298963⟩



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