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The Resource Geometric analysis of hyperbolic differential equations : an introduction, S. Alinhac

Geometric analysis of hyperbolic differential equations : an introduction, S. Alinhac

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
Creator
Subject
Language
eng
Summary
  • "Its self-contained presentation and 'do-it-yourself' 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 so-called 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 space-time"--Provided by publisher
Member of
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
Instantiates
Publication
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
Publication
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

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