An Ingham type proof for a two-grid observability theorem

Michel Mehrenberger; Paola Loreti

ESAIM: Control, Optimisation and Calculus of Variations (2008)

  • Volume: 14, Issue: 3, page 604-631
  • ISSN: 1292-8119

Abstract

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Here, we prove the uniform observability of a two-grid method for the semi-discretization of the 1 D -wave equation for a time T > 2 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.

How to cite

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Mehrenberger, Michel, and Loreti, Paola. "An Ingham type proof for a two-grid observability theorem." ESAIM: Control, Optimisation and Calculus of Variations 14.3 (2008): 604-631. <http://eudml.org/doc/244699>.

@article{Mehrenberger2008,
abstract = {Here, we prove the uniform observability of a two-grid method for the semi-discretization of the $1D$-wave equation for a time $T&gt;2\sqrt\{2\}$; 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.},
author = {Mehrenberger, Michel, Loreti, Paola},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {uniform observability; two-grid method; Ingham type theorem; 1D-wave equation},
language = {eng},
number = {3},
pages = {604-631},
publisher = {EDP-Sciences},
title = {An Ingham type proof for a two-grid observability theorem},
url = {http://eudml.org/doc/244699},
volume = {14},
year = {2008},
}

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
PB - EDP-Sciences
VL - 14
IS - 3
SP - 604
EP - 631
AB - Here, we prove the uniform observability of a two-grid method for the semi-discretization of the $1D$-wave equation for a time $T&gt;2\sqrt{2}$; 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.
LA - eng
KW - uniform observability; two-grid method; Ingham type theorem; 1D-wave equation
UR - http://eudml.org/doc/244699
ER -

References

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