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An Ingham type proof for a two-grid observability theorem

Published online by Cambridge University Press:  21 December 2007

Paola Loreti  and
Michel Mehrenberger
Paola Loreti
Affiliation:
Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Sapienza Università di Roma, Via A. Scarpa 16, 00161 Roma, Italy; loreti@dmmm.uniroma1.it
Michel Mehrenberger
Affiliation:
IRMA, Université Louis Pasteur, 7 rue René Descartes, 67084 Strasbourg, France; mehrenbe@math.u-strasbg.fr
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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. I338 (2004) 413–418]. Our proof follows an Ingham type approach.

Keywords

Uniform observabilitytwo-grid methodIngham type theorem
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 14 , Issue 3 , July 2008 , pp. 604 - 631
Copyright
© EDP Sciences, SMAI, 2007

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References

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