Geometric Analysis of Hyperbolic Differential Equations: An Introduction
Geometric Analysis of Hyperbolic Differential Equations: An Introduction
$73.00
USDIts 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
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
Product details
June 2010Paperback
9780521128223
130 pages
229 × 152 × 7 mm
0.19kg
Available
Table of Contents
- 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.
