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The exponential formula for the Wasserstein metric

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TitleInfo
Title
The exponential formula for the Wasserstein metric
Name (type = personal)
NamePart (type = family)
Craig
NamePart (type = given)
Katy
NamePart (type = date)
1985-
DisplayForm
Katy Craig
Role
RoleTerm (authority = RULIB)
author
Name (type = personal)
NamePart (type = family)
Carlen
NamePart (type = given)
Eric
DisplayForm
Eric Carlen
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
chair
Name (type = personal)
NamePart (type = family)
Sesum
NamePart (type = given)
Natasa
DisplayForm
Natasa Sesum
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Han
NamePart (type = given)
Zheng-Chao
DisplayForm
Zheng-Chao Han
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Gangbo
NamePart (type = given)
Wilfrid
DisplayForm
Wilfrid Gangbo
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
outside member
Name (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (type = corporate)
NamePart
Graduate School - New Brunswick
Role
RoleTerm (authority = RULIB)
school
TypeOfResource
Text
Genre (authority = marcgt)
theses
OriginInfo
DateCreated (qualifier = exact)
2014
DateOther (qualifier = exact); (type = degree)
2014-05
Place
PlaceTerm (type = code)
xx
Language
LanguageTerm (authority = ISO639-2b); (type = code)
eng
Abstract (type = abstract)
Many evolutionary partial differential equations may be rewritten as the gradient flow of an energy functional, a perspective which provides useful estimates on the behavior of solutions. The notion of gradient flow requires both the specification of an energy functional and a metric with respect to which the gradient is taken. In recent years, there has been significant interest in gradient flow on the space of probability measures endowed with the Wasserstein metric. The notion of gradient in this setting in purely formal and rigorous analysis of the gradient flow typically considers a time discretization of the problem known as the discrete gradient flow. In this dissertation, we adapt Crandall and Liggett’s Banach space method to give a new proof of the exponential formula, quantifying the rate at which solutions to the discrete gradient flow converge to solutions of the gradient flow. In the process, we use a new class of metrics—transport metrics—that have stronger convexity properties than the Wasserstein metric to prove an Euler-Lagrange equation characterizing the discrete gradient flow. We then apply these results to give simple proofs of properties of the gradient flow, including the contracting semigroup property and the energy dissipation inequality.
Subject (authority = RUETD)
Topic
Mathematics
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_5520
PhysicalDescription
Form (authority = gmd)
electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
vi, 73 p. : ill.
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Katy Craig
Subject (authority = ETD-LCSH)
Topic
Differential equations, Partial--Numerical solutions
RelatedItem (type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier (type = doi)
doi:10.7282/T3JH3JG8
Genre (authority = ExL-Esploro)
ETD doctoral
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Rights

RightsDeclaration (ID = rulibRdec0006)
The author owns the copyright to this work.
RightsHolder (type = personal)
Name
FamilyName
Craig
GivenName
Katy
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2014-04-15 13:20:25
AssociatedEntity
Name
Katy Craig
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
AssociatedObject
Type
License
Name
Author Agreement License
Detail
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
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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RULTechMD (ID = TECHNICAL1)
ContentModel
ETD
OperatingSystem (VERSION = 5.1)
windows xp
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