The Ivp for the Dispersion Generalized Benjamin-ono Equation in Weighted Sobolev Spaces
نویسندگان
چکیده
We study the initial value problem associated to the dispersion generalized Benjamin-Ono equation. Our aim is to establish well posedness results in weighted Sobolev spaces and to deduce from them some sharp unique continuation properties of solutions to this equation. In particular, we shall establish optimal decay rate for the solutions of this model. RÉSUMÉ. Nous étudions le problème de Cauchy associé à l’équation de Benjamin-Ono avec dispersion généralisée. Notre objectif est d’établir le caractère bien posé de cette équation dans des espaces de Sobolev avec poids et d’en déduire quelques propriétés de prolongement unique pour ses solutions. En particulier, nous établirons un taux de décroissance optimal pour les solutions de ce modèle.
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The Ivp for the Benjamin-ono Equation in Weighted Sobolev Spaces Ii
In this work we continue our study initiated in [10] on the uniqueness properties of real solutions to the IVP associated to the Benjamin-Ono (BO) equation. In particular, we shall show that the uniqueness results established in [10] do not extend to any pair of non-vanishing solutions of the BO equation. Also, we shall prove that the uniqueness result established in [10] under a hypothesis inv...
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