Here, we prove the uniform observability of a two-grid method for the semi-discretization of the -wave equation for a time ; this time, if the observation is made in , 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.
Classification : 35L05, 65M55, 93B07
Mots clés : 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},
pages = {604--631},
publisher = {EDP-Sciences},
volume = {14},
number = {3},
year = {2008},
doi = {10.1051/cocv:2007062},
zbl = {1157.35415},
mrnumber = {2434069},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2007062/}
}
TY - JOUR AU - Mehrenberger, Michel AU - Loreti, Paola TI - An Ingham type proof for a two-grid observability theorem JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2008 DA - 2008/// SP - 604 EP - 631 VL - 14 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2007062/ UR - https://zbmath.org/?q=an%3A1157.35415 UR - https://www.ams.org/mathscinet-getitem?mr=2434069 UR - https://doi.org/10.1051/cocv:2007062 DO - 10.1051/cocv:2007062 LA - en ID - COCV_2008__14_3_604_0 ER -
Mehrenberger, Michel; Loreti, Paola. An Ingham type proof for a two-grid observability theorem. ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 3, pp. 604-631. doi : 10.1051/cocv:2007062. http://www.numdam.org/articles/10.1051/cocv:2007062/
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