Geometric Analysis of Hyperbolic Differential Equations: An Introduction
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.
- Electronic book text | 128 pages
- 18 Dec 2011
- CAMBRIDGE UNIVERSITY PRESS
- Cambridge University Press (Virtual Publishing)
- Cambridge, United Kingdom
About Serge Alinhac
S. Alinhac is Professor in the Department of Mathematics at the University of Paris-Sud 11, Orsay.
'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
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.