Alexandria Digital Research Library

On decay properties of solutions to the IVP for the Benjamin-Ono equation

Author:
Flores, Cynthia Vanessa
Degree Supervisor:
Gustavo Ponce
Place of Publication:
[Santa Barbara, Calif.]
Publisher:
University of California, Santa Barbara
Creation Date:
2014
Issued Date:
2014
Topics:
Mathematics
Keywords:
Weighted Sobolev space
Conserved quantities
Partial Differential Equations
Dispersive equations
Unique continuation
Genres:
Online resources and Dissertations, Academic
Degree Grantor:
University of California, Santa Barbara. Mathematics
Dissertation:
Ph.D.--University of California, Santa Barbara, 2014
Description:

In recent years there has been an intense activity in the study of harmonic analysis and its application to partial differential equations (PDEs). The tools of harmonic analysis assist in the discovery of important properties of certain PDEs; amid these PDEs one finds the study of nonlinear dispersive equations.

In particular, the problems of establishing local and global well-posedness under minimal regularity requirement of the given data, the long-time behavior of local solutions to these models, scattering, blow-up, and the unique continuation properties of the solutions have been extensively studied.

Among the systems considered one finds the Korteweg-de Vries equation, the Schrosystem and the Benjamin-Ono equation, all occurring in different physical problems, mainly nonlinear wave propagation. Furthermore, under certain circumstances, these all admit solitary wave solutions called traveling waves, which have important applications in fiber optics, magnetics and genetics.

In this thesis we investigate unique continuation properties of solutions to the initial value problem associated to the Benjamin-Ono equation given in weighted Sobolev spaces. More precisely, we prove that the uniqueness property based on a decay requirement at three times cannot be lowered to two times even by imposing stronger decay on the initial data.

Physical Description:
1 online resource (63 pages)
Format:
Text
Collection(s):
UCSB electronic theses and dissertations
ARK:
ark:/48907/f3r49nxc
ISBN:
9781321201789
Catalog System Number:
990045115780203776
Rights:
Inc.icon only.dark In Copyright
Copyright Holder:
Cynthia Flores
File Description
Access: Public access
Flores_ucsb_0035D_12134.pdf pdf (Portable Document Format)