The Resource Geometric analysis of hyperbolic differential equations : an introduction, S. Alinhac
Geometric analysis of hyperbolic differential equations : an introduction, S. Alinhac
Resource Information
The item Geometric analysis of hyperbolic differential equations : an introduction, S. Alinhac represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of MissouriSt. Louis Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Geometric analysis of hyperbolic differential equations : an introduction, S. Alinhac represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of MissouriSt. Louis Libraries.
This item is available to borrow from 1 library branch.
 Summary

 "Its selfcontained presentation and 'doityourself' approach make this the perfect guide for graduate students and researchers wishing to access recent literature in the field of nonlinear wave equations and general relativity. It introduces all of the key tools and concepts from Lorentzian geometry (metrics, null frames, deformation tensors, etc.) and provides complete elementary proofs. The author also discusses applications to topics in nonlinear equations, including null conditions and stability of Minkowski space. No previous knowledge of geometry or relativity is required"Provided by publisher
 "The field of nonlinear hyperbolic equations or systems has seen a tremendous development since the beginning of the 1980s. We are concentrating here on multidimensional situations, and on quasilinear equations or systems, that is, when the coefficients of the principal part depend on the unknown function itself. The pioneering works by F. John, D. Christodoulou, L. Hörmander, S. Klainerman, A. Majda and many others have been devoted mainly to the questions of blowup, lifespan, shocks, global existence, etc. Some overview of the classical results can be found in the books of Majda [42] and Hörmander [24]. On the other hand, Christodoulou and Klainerman [18] proved in around 1990 the stability of Minkowski space, a striking mathematical result about the Cauchy problem for the Einstein equations. After that, many works have dealt with diagonal systems of quasilinear wave equations, since this is what Einstein equations reduce to when written in the socalled harmonic coordinates. The main feature of this particular case is that the (scalar) principal part of the system is a wave operator associated to a unique Lorentzian metric on the underlying spacetime"Provided by publisher
 Language
 eng
 Extent
 1 online resource (ix, 118 pages).
 Contents

 1. Introduction
 2. Metrics and frames
 3. Computing with frames
 4. Energy inequalities and frames
 5. The good components
 6. Pointwise estimates and commutations
 7. Frames and curvature
 8. Nonlinear equations, a priori estimates and induction
 9. Applications to some quasilinear hyperbolic problems
 References
 Index
 Isbn
 9781139107198
 Label
 Geometric analysis of hyperbolic differential equations : an introduction
 Title
 Geometric analysis of hyperbolic differential equations
 Title remainder
 an introduction
 Statement of responsibility
 S. Alinhac
 Subject

 Differential equations, Hyperbolic
 Geometry, Differential
 Geometry, Differential
 Hyperbolische Differentialgleichung
 MATHEMATICS  Differential Equations  Partial
 Nichtlineare Wellengleichung
 Nonlinear wave equations
 Nonlinear wave equations
 Quantum theory
 Quantum theory
 Differential equations, Hyperbolic
 Language
 eng
 Summary

 "Its selfcontained presentation and 'doityourself' approach make this the perfect guide for graduate students and researchers wishing to access recent literature in the field of nonlinear wave equations and general relativity. It introduces all of the key tools and concepts from Lorentzian geometry (metrics, null frames, deformation tensors, etc.) and provides complete elementary proofs. The author also discusses applications to topics in nonlinear equations, including null conditions and stability of Minkowski space. No previous knowledge of geometry or relativity is required"Provided by publisher
 "The field of nonlinear hyperbolic equations or systems has seen a tremendous development since the beginning of the 1980s. We are concentrating here on multidimensional situations, and on quasilinear equations or systems, that is, when the coefficients of the principal part depend on the unknown function itself. The pioneering works by F. John, D. Christodoulou, L. Hörmander, S. Klainerman, A. Majda and many others have been devoted mainly to the questions of blowup, lifespan, shocks, global existence, etc. Some overview of the classical results can be found in the books of Majda [42] and Hörmander [24]. On the other hand, Christodoulou and Klainerman [18] proved in around 1990 the stability of Minkowski space, a striking mathematical result about the Cauchy problem for the Einstein equations. After that, many works have dealt with diagonal systems of quasilinear wave equations, since this is what Einstein equations reduce to when written in the socalled harmonic coordinates. The main feature of this particular case is that the (scalar) principal part of the system is a wave operator associated to a unique Lorentzian metric on the underlying spacetime"Provided by publisher
 Cataloging source
 N$T
 http://library.link/vocab/creatorName
 Alinhac, S.
 Dewey number
 515/.3535
 Index
 index present
 LC call number
 QA927
 LC item number
 .A3886 2010eb
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 London Mathematical Society lecture note series
 Series volume
 374
 http://library.link/vocab/subjectName

 Nonlinear wave equations
 Differential equations, Hyperbolic
 Quantum theory
 Geometry, Differential
 MATHEMATICS
 Differential equations, Hyperbolic
 Geometry, Differential
 Nonlinear wave equations
 Quantum theory
 Hyperbolische Differentialgleichung
 Nichtlineare Wellengleichung
 Label
 Geometric analysis of hyperbolic differential equations : an introduction, S. Alinhac
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 1. Introduction  2. Metrics and frames  3. Computing with frames  4. Energy inequalities and frames  5. The good components  6. Pointwise estimates and commutations  7. Frames and curvature  8. Nonlinear equations, a priori estimates and induction  9. Applications to some quasilinear hyperbolic problems  References  Index
 Control code
 802261816
 Dimensions
 unknown
 Extent
 1 online resource (ix, 118 pages).
 File format
 unknown
 Form of item
 online
 Isbn
 9781139107198
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 9786613296030
 http://library.link/vocab/ext/overdrive/overdriveId
 329603
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)802261816
 Label
 Geometric analysis of hyperbolic differential equations : an introduction, S. Alinhac
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 1. Introduction  2. Metrics and frames  3. Computing with frames  4. Energy inequalities and frames  5. The good components  6. Pointwise estimates and commutations  7. Frames and curvature  8. Nonlinear equations, a priori estimates and induction  9. Applications to some quasilinear hyperbolic problems  References  Index
 Control code
 802261816
 Dimensions
 unknown
 Extent
 1 online resource (ix, 118 pages).
 File format
 unknown
 Form of item
 online
 Isbn
 9781139107198
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 9786613296030
 http://library.link/vocab/ext/overdrive/overdriveId
 329603
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)802261816
Subject
 Differential equations, Hyperbolic
 Geometry, Differential
 Geometry, Differential
 Hyperbolische Differentialgleichung
 MATHEMATICS  Differential Equations  Partial
 Nichtlineare Wellengleichung
 Nonlinear wave equations
 Nonlinear wave equations
 Quantum theory
 Quantum theory
 Differential equations, Hyperbolic
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.umsl.edu/portal/Geometricanalysisofhyperbolicdifferential/5aKBb0u32I8/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.umsl.edu/portal/Geometricanalysisofhyperbolicdifferential/5aKBb0u32I8/">Geometric analysis of hyperbolic differential equations : an introduction, S. Alinhac</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.umsl.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.umsl.edu/">University of MissouriSt. Louis Libraries</a></span></span></span></span></div>