Geometric Analysis of Hyperbolic Differential Equations: An Introduction: 374 (London Mathematical Society Lecture Note Series, Series Number 374)
Cambridge University Press, 5/20/2010
EAN 9780521128223, ISBN10: 0521128226
Paperback, 130 pages, 22.9 x 15.2 x 0.8 cm
Language: English
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.
Preface
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.