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Issue ESAIM: Proc.
Volume 25, 2008
Paris-sud working group on modelling and scientific computing 2007-2008
Page(s) 58 - 79
DOI http://dx.doi.org/10.1051/proc:082505
Published online 16 January 2009

ESAIM: Proc., 2008, Vol. 25, pp. 58-79
DOI: 10.1051/proc:082505

Observabilité uniforme de l'équation des ondes 1D

Paola Loreti1 and Michel Mehrenberger2

1  Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Sapienza Universita' di Roma, Via A. Scarpa 16, 00161 Roma, Italy, loreti@dmmm.uniroma1.it
2  ULP-IRMA 7, rue René Descartes, 67084 Strasbourg, mehrenbe@math.u-strasbg.fr


Published online: 16 January 2009

Abstract
This proceedings is a complement of [7]. In [7], new Ingham type theorems have been developped in order to establish the uniform observability of the wave equation in 1D. We gather here in a self-contained and compact form several results obtained by the mean of discrete multipliers. In a second part, we give an example of Ingham type inequality where the position of the interval is a key point in the determination of the optimal time. This example enforces the idea that such phenomenon, already mentionned in [7], can occur.


Résumé
Cet acte est un complément de [7]. Dans [7], de nouveaux théorèmes d'Ingham ont été établis pour obtenir l'observabilité uniforme de l'équation des ondes 1D. Nous rassemblons ici, sous forme compacte et auto-contenue, plusieurs résultats obtenus à l'aide des multiplicateurs discrets. D'autre part, nous établissons un exemple d'inégalité de type Ingham où la position de l'intervalle joue un rôle dans la détermination du temps optimal, ce qui n'est habituellement pas le cas. L'exemple en question renforce l'idée que ce phénomène, déjà évoqué dans [7], peut apparaître.



© EDP Sciences, ESAIM 2008


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