000			03622cam a2200397 a 4500
001			16050138
003			OSt
005			20150408114018.0
008			100111s2010 enk b 001 0 eng
010			_a 2010001099
015			_aGBB004211 _2bnb
016	7		_a015462031 _2Uk
020			_a9780521128223 (pbk.)
020			_a0521128226 (pbk.)
035			_a(OCoLC)ocn489001674
040			_aDLC _cDLC _dUKM _dBTCTA _dYDXCP _dBWKUK _dCDX _dBWK _dBWX _dRRR _dUWO _dDLC
050	0	0	_aQA927 _b.A3886 2010
082	0	0	_a515.3535 _222
100	1		_aAlinhac, S. _q(Serge) _914513
245	1	0	_aGeometric analysis of hyperbolic differential equations : _ban introduction / _cS. Alinhac.
260			_aCambridge, UK ; _aNew York : _bCambridge University Press, _c2010.
300			_aix, 118 p. ; _c23 cm.
490	1		_aLondon Mathematical Society lecture note series ; _v374
504			_aIncludes bibliographical references and index.
505	0		_a1. 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.
520			_a"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.
520			_a"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.
650		0	_aNonlinear wave equations. _914514
650		0	_aDifferential equations, Hyperbolic. _914515
650		0	_aQuantum theory. _98263
650		0	_aGeometry, Differential. _914516
830		0	_aLondon Mathematical Society lecture note series ; _v374. _914517
856	4	2	_3Cover image _uhttp://assets.cambridge.org/97805211/28223/cover/9780521128223.jpg
942			_2ddc _cBOOK
999			_c21742 _d256242