The Resource Lectures on the energy critical nonlinear wave equation, Carlos E. Kenig
Lectures on the energy critical nonlinear wave equation, Carlos E. Kenig
Resource Information
The item Lectures on the energy critical nonlinear wave equation, Carlos E. Kenig represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Lectures on the energy critical nonlinear wave equation, Carlos E. Kenig represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 Summary
 This monograph deals with recent advances in the study of the longtime asymptotics of large solutions to critical nonlinear dispersive equations. The first part of the monograph describes, in the context of the energy critical wave equation, the "concentrationcompactness/rigidity theorem method" introduced by C. Kenig and F. Merle. This approach has become the canonical method for the study of the "global regularity and wellposedness" conjecture (defocusing case) and the "groundstate" conjecture (focusing case) in critical dispersive problems. The second part of the monograph describes the "channel of energy" method, introduced by T. Duyckaerts, C. Kenig, and F. Merle, to study soliton resolution for nonlinear wave equations. This culminates in a presentation of the proof of the soliton resolution conjecture, for the threedimensional radial focusing energy critical wave equation. It is the intent that the results described in this book will be a model for what to strive for in the study of other nonlinear dispersive equations. A copublication of the AMS and CBMS. Provided by publisher
 Language
 eng
 Extent
 xiii, 161 pages
 Note
 "NSF/CBMS Regional Conference in Mathematical Sciences on the Energy Critical Nonlinear Wave Equation held at Kansas State University in June 2013"Title page verso
 Contents

 The Local Theory of the Cauchy Problem
 The "Road Map": The Concentration Compactness/Rigidity Theorem Method for Critical Problems I
 The "Road Map": The Concentration Compactness/Rigidity Theorem Method for Critical Problems II
 Properties of Compact Solutions and Some More Rigidity Theorems, with Applications to an Extension of Theorem 2.6
 Proof of the Rigidity Theorems
 Type II BlowUp Solutions
 Channels of Energy and Outer Energy Lower Bounds
 Universal Type II Blowup Profiles
 Soliton Resolution for Radial Solutions to (NLW), I
 Universal Type II Blowup Profiles
 Soliton Resolution for Radial Solutions to (NLW), II
 Universal Type II Blowup Profiles
 Soliton Resolution for Radial Solutions to (NLW), III
 Isbn
 9781470420147
 Label
 Lectures on the energy critical nonlinear wave equation
 Title
 Lectures on the energy critical nonlinear wave equation
 Statement of responsibility
 Carlos E. Kenig
 Subject

 Nonlinear wave equations
 Partial differential equations  Equations of mathematical physics and other areas of application  None of the above, but in this section
 Partial differential equations  Hyperbolic equations and systems  Semilinear secondorder hyperbolic equations
 Wavemotion, Theory of
 Wavemotion, Theory of
 Nonlinear partial differential operators
 Nonlinear partial differential operators
 Language
 eng
 Summary
 This monograph deals with recent advances in the study of the longtime asymptotics of large solutions to critical nonlinear dispersive equations. The first part of the monograph describes, in the context of the energy critical wave equation, the "concentrationcompactness/rigidity theorem method" introduced by C. Kenig and F. Merle. This approach has become the canonical method for the study of the "global regularity and wellposedness" conjecture (defocusing case) and the "groundstate" conjecture (focusing case) in critical dispersive problems. The second part of the monograph describes the "channel of energy" method, introduced by T. Duyckaerts, C. Kenig, and F. Merle, to study soliton resolution for nonlinear wave equations. This culminates in a presentation of the proof of the soliton resolution conjecture, for the threedimensional radial focusing energy critical wave equation. It is the intent that the results described in this book will be a model for what to strive for in the study of other nonlinear dispersive equations. A copublication of the AMS and CBMS. Provided by publisher
 Cataloging source
 DLC
 http://library.link/vocab/creatorDate
 1953
 http://library.link/vocab/creatorName
 Kenig, Carlos E.
 Dewey number
 515/.353
 Illustrations
 illustrations
 Index
 no index present
 LC call number
 QA329.42
 LC item number
 .K46 2015
 Literary form
 non fiction
 Nature of contents
 bibliography
 http://library.link/vocab/relatedWorkOrContributorDate
 2013
 http://library.link/vocab/relatedWorkOrContributorName

 Conference Board of the Mathematical Sciences
 National Science Foundation (U.S.)
 NSF/CBMS Regional Conference in Mathematical Sciences on the Energy Critical Nonlinear Wave Equation
 Series statement
 CBMS regional conference series in mathematics
 Series volume
 number 122
 http://library.link/vocab/subjectName

 Nonlinear partial differential operators
 Nonlinear wave equations
 Wavemotion, Theory of
 Nonlinear partial differential operators
 Wavemotion, Theory of
 Partial differential equations  Hyperbolic equations and systems  Semilinear secondorder hyperbolic equations
 Partial differential equations  Equations of mathematical physics and other areas of application  None of the above, but in this section
 Nonlinear partial differential operators
 Wavemotion, Theory of
 Label
 Lectures on the energy critical nonlinear wave equation, Carlos E. Kenig
 Note
 "NSF/CBMS Regional Conference in Mathematical Sciences on the Energy Critical Nonlinear Wave Equation held at Kansas State University in June 2013"Title page verso
 Bibliography note
 Includes bibliographical references (pages 157161)
 Carrier category
 volume
 Carrier category code

 nc
 Carrier MARC source
 rdacarrier.
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent.
 Contents
 The Local Theory of the Cauchy Problem  The "Road Map": The Concentration Compactness/Rigidity Theorem Method for Critical Problems I  The "Road Map": The Concentration Compactness/Rigidity Theorem Method for Critical Problems II  Properties of Compact Solutions and Some More Rigidity Theorems, with Applications to an Extension of Theorem 2.6  Proof of the Rigidity Theorems  Type II BlowUp Solutions  Channels of Energy and Outer Energy Lower Bounds  Universal Type II Blowup Profiles  Soliton Resolution for Radial Solutions to (NLW), I  Universal Type II Blowup Profiles  Soliton Resolution for Radial Solutions to (NLW), II  Universal Type II Blowup Profiles  Soliton Resolution for Radial Solutions to (NLW), III
 Control code
 899952223
 Dimensions
 26 cm
 Extent
 xiii, 161 pages
 Isbn
 9781470420147
 Lccn
 2015000062
 Media category
 unmediated
 Media MARC source
 rdamedia.
 Media type code

 n
 System control number
 (OCoLC)899952223
 Label
 Lectures on the energy critical nonlinear wave equation, Carlos E. Kenig
 Note
 "NSF/CBMS Regional Conference in Mathematical Sciences on the Energy Critical Nonlinear Wave Equation held at Kansas State University in June 2013"Title page verso
 Bibliography note
 Includes bibliographical references (pages 157161)
 Carrier category
 volume
 Carrier category code

 nc
 Carrier MARC source
 rdacarrier.
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent.
 Contents
 The Local Theory of the Cauchy Problem  The "Road Map": The Concentration Compactness/Rigidity Theorem Method for Critical Problems I  The "Road Map": The Concentration Compactness/Rigidity Theorem Method for Critical Problems II  Properties of Compact Solutions and Some More Rigidity Theorems, with Applications to an Extension of Theorem 2.6  Proof of the Rigidity Theorems  Type II BlowUp Solutions  Channels of Energy and Outer Energy Lower Bounds  Universal Type II Blowup Profiles  Soliton Resolution for Radial Solutions to (NLW), I  Universal Type II Blowup Profiles  Soliton Resolution for Radial Solutions to (NLW), II  Universal Type II Blowup Profiles  Soliton Resolution for Radial Solutions to (NLW), III
 Control code
 899952223
 Dimensions
 26 cm
 Extent
 xiii, 161 pages
 Isbn
 9781470420147
 Lccn
 2015000062
 Media category
 unmediated
 Media MARC source
 rdamedia.
 Media type code

 n
 System control number
 (OCoLC)899952223
Subject
 Nonlinear wave equations
 Partial differential equations  Equations of mathematical physics and other areas of application  None of the above, but in this section
 Partial differential equations  Hyperbolic equations and systems  Semilinear secondorder hyperbolic equations
 Wavemotion, Theory of
 Wavemotion, Theory of
 Nonlinear partial differential operators
 Nonlinear partial differential operators
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