Abstract/Details

Global well posedness for some dispersive partial differential equations


2004 2004

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Abstract (summary)

In this thesis we study the global in time solutions of some dispersive partial differential equations (pdes). More precisely in this work we consider the nonlinear Schrödinger equation, the generalized Korteweg de Vries equation, and the Klein-Gordon-Schrödinger system. For these equations, a local in time solution is known to exist. Using a modified functional that is closely related to the original energy functional of the equations, we show how to iterate the local result and prove that the solutions exist for all time. Our proofs also demonstrate polynomial in time bounds on the solutions within an appropriate function space.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences, Dispersive partial differential equations, Schrodinger equation
Title
Global well posedness for some dispersive partial differential equations
Author
Tzirakis, Nikolaos I.
Number of pages
117
Publication year
2004
Degree date
2004
School code
0118
Source
DAI-B 65/11, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780496133086, 049613308X
Advisor
Nahmod, Andrea R.
University/institution
University of Massachusetts Amherst
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3152755
ProQuest document ID
305176794
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/305176794
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