Unique continuation properties for nonlinear dispersive equations.

Abstract

The nonlinear dispersive equations is a branch of the partial differential equations arising in the modeling of the propagation of nonlinear waves.One interesting problem regarding this family of equations concerns with the study of the so-called unique continuation property (UCP). In this project our main interest is to look for sufficient conditions on the solutions of these equations so that the behavior of thesolutions in two or more different times imply that the solutions vanish in the whole domain of existence of the solutions. This problem has been studied intensively in the last few years.In this direction there have been obtained important results for the Korteweg-de Vries, Nonlinear Schrodinger and Benjamin-Onoequations. We will study this property and other related properties for solutions of some relevant models that have not been treated in the literature.