03622cam a2200397 a 4500 16050138 OSt 20150408114018.0 100111s2010 enk b 001 0 eng 2010001099 GBB004211 bnb 015462031 Uk 9780521128223 (pbk.) 0521128226 (pbk.) (OCoLC)ocn489001674 DLC DLC UKM BTCTA YDXCP BWKUK CDX BWK BWX RRR UWO DLC QA927 .A3886 2010 515.3535 22 Alinhac, S. (Serge) 14513 Geometric analysis of hyperbolic differential equations : an introduction / S. Alinhac. Cambridge, UK ; New York : Cambridge University Press, 2010. ix, 118 p. ; 23 cm. London Mathematical Society lecture note series ; 374 Includes bibliographical references and index. 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. "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. Nonlinear wave equations. 14514 Differential equations, Hyperbolic. 14515 Quantum theory. 8263 Geometry, Differential. 14516 London Mathematical Society lecture note series ; 374. 14517 Cover image http://assets.cambridge.org/97805211/28223/cover/9780521128223.jpg ddc BOOK 21742 256242 0 2013-03-10 0 0 515.3535 A S G 2012-05-20 EMF 00086546 EMF 2013-03-10 00:00:00 BOOK ddc 0 0 2013-03-10 0 0 515.3535 A S G 2012-05-20 EMF 00086547 EMF 2013-03-10 00:00:00 BOOK ddc 0 0 2013-03-10 0 0 515.3535 A S G 2012-05-31 SZM 00087747 SZM 2013-03-10 00:00:00 BOOK ddc 0 0 2013-03-10 0 0 515.3535 A S G 2012-05-31 SZM 00087748 SZM 2013-03-10 00:00:00 BOOK ddc 0 0 2013-03-10 0 0 515.3535 A S G 2012-06-01 EZF 00086965 EZF 2013-03-10 00:00:00 BOOK ddc 0 0 2013-03-10 0 0 515.3535 A S G 2012-06-01 EZF 00086964 EZF 2013-03-10 00:00:00 BOOK ddc 0 0 2013-03-10 0 0 515.3535 A S G 2012-06-04 SHF 00088056 SHF 2013-03-10 00:00:00 BOOK ddc 0 0 2013-03-10 0 0 515.3535 A S G 2012-06-04 SHF 00088057 SHF 2013-03-10 00:00:00 BOOK ddc 0