Inégalité d'observabilité du type logarithmique et estimation de la fonction de coût des solutions des équations hyperboliques
ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 2, pp. 318-342.

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.

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.

DOI : https://doi.org/10.1051/cocv:2007052
Classification : 35B37,  93B05,  93B07,  35L20
Mots clés : problème hyberbolique, contrôle, fonction de coût, inégalité de Carleman
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     title = {In\'egalit\'e d'observabilit\'e du type logarithmique et estimation de la fonction de co\^ut des solutions des \'equations hyperboliques},
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Ouksel, Leila. Inégalité d'observabilité du type logarithmique et estimation de la fonction de coût des solutions des équations hyperboliques. ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 2, pp. 318-342. doi : 10.1051/cocv:2007052. http://www.numdam.org/articles/10.1051/cocv:2007052/

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