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Multi-channel scattering theory: large time asymptotics of Schrödinger type equations with general data
Descriptive
TitleInfo
Title
Multi-channel scattering theory: large time asymptotics of Schrödinger type equations with general data
TitleInfo
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Title
Multi-channel scattering theory: large time asymptotics of Schrodinger type equations with general data
Name
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Wu
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Xiaoxu
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Xiaoxu Wu
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author
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Soffer
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Advisory Committee
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chair
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Cakoni
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Fioralba
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Fioralba Cakoni
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member
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Jauslin
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Ian
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Ian Jauslin
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Advisory Committee
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member
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Kiessling
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Michael
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Michael Kiessling
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Advisory Committee
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member
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Rutgers University
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School of Graduate Studies
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school
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theses
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2023
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2023-05
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2023
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English
Abstract
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This thesis appears to focus on scattering theory for both Schrödinger-type equations and Klein-Gordon equations. Chapter 1 provides an introduction to the background of the thesis, while Chapter 2 investigates the long-time behavior of solutions to the Schrödinger equation. Chapter 3 focuses on the construction of solutions to Schrödinger equations with non-trivial weakly localized parts, asymptotic self-similar solutions as time goes to infinity. Chapter 4 studies the long-time behavior of solutions to Klein-Gordon equations. In Chapter 5, the author presents a proof of Local Decay Estimates for Schrödinger-type equations. Finally, Chapter 6 establishes the $L^p$ boundedness of wave operators for linear Schrödinger equations with time-dependent potentials and provides applications of this result to nonlinear dispersive equations and Hartree nonlinear Schrödinger equations.
Subject
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Topic
Mathematics
Subject
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Topic
Scattering (Mathematics)
Subject
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Topic
Schrödinger equation
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Rutgers University Electronic Theses and Dissertations
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http://dissertations.umi.com/gsnb.rutgers:12381
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277 pages
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Ph.D.
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Includes bibliographical references
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School of Graduate Studies Electronic Theses and Dissertations
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rucore10001600001
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Identifier
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doi:10.7282/t3-qeas-fj24
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Rights
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The author owns the copyright to this work.
RightsHolder
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Name
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Wu
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Xiaoxu
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2023-04-27T16:08:33
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Xiaoxu Wu
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Rutgers University. School of Graduate Studies
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Author Agreement License
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
Copyright
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Copyright protected
Availability
Status
Open
Reason
Permission or license
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2023-03-21T12:14:50
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