An Ingham type proof for a two-grid observability theorem

Paola Loreti (1) , Michel Mehrenberger (2, 3)

1 Dipartimento di Scienze di Base e Applicate per l'Ingegneria
2 CALVI - Scientific computation and visualization
3 IRMA - Institut de Recherche Mathématique Avancée

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.

Domaines: Mathématiques [math]

Paola Loreti, Michel Mehrenberger. An Ingham type proof for a two-grid observability theorem. ESAIM: Control, Optimisation and Calculus of Variations, 2008, ⟨10.1051/cocv:2007062⟩. ⟨hal-01298963⟩