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THE IVP FOR THE DISPERSION GENERALIZED BENJAMIN-ONO EQUATION IN WEIGHTED SOBOLEV
 

Summary: THE IVP FOR THE DISPERSION GENERALIZED
BENJAMIN-ONO EQUATION IN WEIGHTED SOBOLEV
SPACES
GERMŽAN FONSECA, FELIPE LINARES, AND GUSTAVO PONCE
Abstract. We study the initial value problem associated to the disper-
sion 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.
RŽESUMŽE. Nous Žetudions le probl`eme de Cauchy associŽe `a l'Žequation de
Benjamin-Ono avec dispersion gŽenŽeralisŽee. Notre objectif est d'Žetablir le
caract`ere bien posŽe de cette Žequation dans des espaces de Sobolev avec
poids et d'en dŽeduire quelques propriŽetŽes de prolongement unique pour
ses solutions. En particulier, nous Žetablirons un taux de dŽecroissance
optimal pour les solutions de ce mod`ele.
1. Introduction
This work is concerned with the initial value problem (IVP) for the dis-
persion generalized Benjamin-Ono (DGBO) equation
tu + D1+axu + uxu = 0, t, x R, 0 < a < 1,

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics