[Estimées d'observabilité uniformes pour l'équation des ondes unidimensionnelle et méthode du choix aléatoire]
Dans cette Note, nous considérons l'équation des ondes unidimensionnelle discrétisée selon la méthode du choix aléatoire due à J. Glimm. Nous établissons que pour presque tout choix de la variable aléatoire, l'estimée d'observabilité pour cette équation est vraie asymptotiquement, uniformément en les paramètres de discrétisation.
In this Note, we consider the 1-dimensional wave equation, discretized by means of Glimm's random choice method. We prove that for almost every choice of the random parameter, the observability estimate is true asymptotically, uniformly with respect to the discretization parameters.
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@article{CRMATH_2009__347_9-10_505_0,
author = {Coron, Jean-Michel and Ervedoza, Sylvain and Glass, Olivier},
title = {Uniform observability estimates for the {1-D} discretized wave equation and the random choice method},
journal = {Comptes Rendus. Math\'ematique},
pages = {505--510},
publisher = {Elsevier},
volume = {347},
number = {9-10},
year = {2009},
doi = {10.1016/j.crma.2009.03.012},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/j.crma.2009.03.012/}
}
TY - JOUR AU - Coron, Jean-Michel AU - Ervedoza, Sylvain AU - Glass, Olivier TI - Uniform observability estimates for the 1-D discretized wave equation and the random choice method JO - Comptes Rendus. Mathématique PY - 2009 SP - 505 EP - 510 VL - 347 IS - 9-10 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2009.03.012/ DO - 10.1016/j.crma.2009.03.012 LA - en ID - CRMATH_2009__347_9-10_505_0 ER -
%0 Journal Article %A Coron, Jean-Michel %A Ervedoza, Sylvain %A Glass, Olivier %T Uniform observability estimates for the 1-D discretized wave equation and the random choice method %J Comptes Rendus. Mathématique %D 2009 %P 505-510 %V 347 %N 9-10 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2009.03.012/ %R 10.1016/j.crma.2009.03.012 %G en %F CRMATH_2009__347_9-10_505_0
Coron, Jean-Michel; Ervedoza, Sylvain; Glass, Olivier. Uniform observability estimates for the 1-D discretized wave equation and the random choice method. Comptes Rendus. Mathématique, Tome 347 (2009) no. 9-10, pp. 505-510. doi : 10.1016/j.crma.2009.03.012. http://archive.numdam.org/articles/10.1016/j.crma.2009.03.012/
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