An Ingham type proof for a two-grid observability theorem
ESAIM: Control, Optimisation and Calculus of Variations, Volume 14 (2008) no. 3, p. 604-631

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 $\left(-T/2,T/2\right)$, 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.

DOI : https://doi.org/10.1051/cocv:2007062
Classification:  35L05,  65M55,  93B07
Keywords: uniform observability, two-grid method, Ingham type theorem
@article{COCV_2008__14_3_604_0,
author = {Mehrenberger, Michel and Loreti, Paola},
title = {An Ingham type proof for a two-grid observability theorem},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {14},
number = {3},
year = {2008},
pages = {604-631},
doi = {10.1051/cocv:2007062},
zbl = {1157.35415},
mrnumber = {2434069},
language = {en},
url = {http://www.numdam.org/item/COCV_2008__14_3_604_0}
}

Mehrenberger, Michel; Loreti, Paola. An Ingham type proof for a two-grid observability theorem. ESAIM: Control, Optimisation and Calculus of Variations, Volume 14 (2008) no. 3, pp. 604-631. doi : 10.1051/cocv:2007062. http://www.numdam.org/item/COCV_2008__14_3_604_0/

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