Unicité forte à l'infini pour KdV

Robbiano, Luc

doi:10.1051/cocv:2002031

Robbiano, Luc

ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 933-939.

Résumé
Abstract

Dans ce papier nous prouvons que si une solution de KdV est suffisamment décroissante à l’infini (c’est-à-dire comme e $^{- x^{α}}$ où $α > 9 / 4$ ) et si la donnée de Cauchy est nulle pour $x$ assez grand alors la solution est nulle. Ce résultat est la conséquence d’une inégalité de Carleman adaptée à la décroissance de la solution à l’infini.

In this paper we prove that if a solution of KdV equation decreases fast enough (i.e. like e $^{- x^{α}}$ where $α > 9 / 4$ ) and if the Cauchy data is null for $x$ large enough then the solution is zero. We prove a Carleman’s estimate and the uniqueness result follows.

Zbl

DOI : 10.1051/cocv:2002031

Classification : 35Q53, 35A07
Mots-clés : Korteweg de Vries, unicité, inégalité de Carleman

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     title = {Unicit\'e forte \`a l'infini pour {KdV}},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {933--939},
     publisher = {EDP-Sciences},
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Robbiano, Luc. Unicité forte à l'infini pour KdV. ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 933-939. doi : 10.1051/cocv:2002031. https://www.numdam.org/articles/10.1051/cocv:2002031/

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