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Geometric Analysis of Hyperbolic Differential Equations: An Introduction


Part of London Mathematical Society Lecture Note Series

  • Date Published: May 2010
  • availability: Available
  • format: Paperback
  • isbn: 9780521128223

£ 48.99

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About the Authors
  • 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.

    • No prerequisites - easily accessible to analysts in the field of PDEs
    • Elementary proofs serve as exercises for the reader
    • Provides all the necessary mathematical tools of Lorentzian geometry
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    Reviews & endorsements

    'This book provides an excellent introduction to nonlinear wave equations, and it can be recommended to anyone who wants to access the recent mathematical literature on this subject.' Zentralblatt MATH

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    Product details

    • Date Published: May 2010
    • format: Paperback
    • isbn: 9780521128223
    • length: 130 pages
    • dimensions: 229 x 152 x 7 mm
    • weight: 0.19kg
    • availability: Available
  • Table of 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

  • Author

    S. Alinhac, Université de Paris XI
    S. Alinhac is Professor in the Department of Mathematics at the University of Paris-Sud 11, Orsay.

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