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Issue ESAIM: COCV
Volume 14, Number 2, April-June 2008
Page(s) 318 - 342
DOI 10.1051/cocv:2007052
Published online 20 March 2008

ESAIM: COCV, Vol. 14, N°2, pp. 318-342
DOI: 10.1051/cocv:2007052

Inégalité d'observabilité du type logarithmique et estimation de la fonction de coût des solutions des équations hyperboliques

Leila Ouksel

Université de Paris Sud, Mathématiques, Bât. 425, 91405 Orsay cedex, France; Leila.Ouksel@math.u-psud.fr


(Received November 6, 2005. Revised June 16, 2006. Published online October 13, 2007.)

Abstract
This work proposes a logarithmic estimation of the initial values of the solution u of a hyperbolic problem, with Neumann boundary conditions, using the trace of u restricted to the neighbourhood of the boundary, during a time sufficiently large for estimating the cost function of the problem.


Résumé
Dans ce travail, nous donnons une estimation logarithmique des données de la solution u, d'un problème hyperbolique avec condition aux limites de type Neumann, par la trace de u restreinte à un ouvert du bord, pendant un temps suffisamment grand qui nous permet d'estimer la fonction de coût de ce problème.


Mathematics Subject Classification. 35B37, 93B05, 93B07, 35L20

Key words: Problème hyberbolique, contrôle, fonction de coût, inégalité de Carleman


© EDP Sciences, SMAI 2008


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