An Ingham type proof for a two-grid observability theorem

Paola Loreti; Michel Mehrenberger

ESAIM: Control, Optimisation and Calculus of Variations (2007)

  • 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 1D-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. I338 (2004) 413–418]. Our proof follows an Ingham type approach.

How to cite

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Loreti, Paola, and Mehrenberger, Michel. "An Ingham type proof for a two-grid observability theorem." ESAIM: Control, Optimisation and Calculus of Variations 14.3 (2007): 604-631. <http://eudml.org/doc/90886>.

@article{Loreti2007,
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. },
author = {Loreti, Paola, Mehrenberger, Michel},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Uniform observability; two-grid method; Ingham type theorem; uniform observability; 1D-wave equation},
language = {eng},
month = {12},
number = {3},
pages = {604-631},
publisher = {EDP Sciences},
title = {An Ingham type proof for a two-grid observability theorem},
url = {http://eudml.org/doc/90886},
volume = {14},
year = {2007},
}

TY - JOUR
AU - Loreti, Paola
AU - Mehrenberger, Michel
TI - An Ingham type proof for a two-grid observability theorem
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2007/12//
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 $T>2\sqrt{2}$; 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.
LA - eng
KW - Uniform observability; two-grid method; Ingham type theorem; uniform observability; 1D-wave equation
UR - http://eudml.org/doc/90886
ER -

References

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