Geodesic
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

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Here, we prove the uniform observability of a two-grid method for the semi-discretization of the 1D-wave equation for a time T>22; 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.

DOI : 10.1051/cocv:2007062
Classification : 35L05, 65M55, 93B07
Keywords: uniform observability, two-grid method, Ingham type theorem 
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     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},
     mrnumber = {2434069},
     zbl = {1157.35415},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2007062/}
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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

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