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Geometric analysis of hyperbolic dif...

Alinhac, S.

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Geometric analysis of hyperbolic differential equations : = an introduction /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Geometric analysis of hyperbolic differential equations :/ S. Alinhac.
其他題名:	an introduction /
作者:	Alinhac, S.
出版者:	Cambridge, UK ;Cambridge University Press, : 2010.,
面頁冊數:	ix, 118 p. ;23 cm.
內容註:	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.
標題:	Nonlinear wave equations. -
電子資源:	http://assets.cambridge.org/97805211/28223/cover/9780521128223.jpg
ISBN:	9780521128223 (pbk.) :

Geometric analysis of hyperbolic differential equations : = an introduction /
Alinhac, S.

Geometric analysis of hyperbolic differential equations :an introduction /S. Alinhac. - Cambridge, UK ;Cambridge University Press,2010. - ix, 118 p. ;23 cm. - London Mathematical Society lecture note series ;374. - London Mathematical Society lecture note series ;359..

Includes bibliographical references (p. 114-116) 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.

ISBN: 9780521128223 (pbk.) :US50.00

LCCN: 2010001099

Nat. Bib. No.: GBB004211bnb

Nat. Bib. Agency Control No.: 015462031UkSubjects--Topical Terms:

673901
Nonlinear wave equations.

LC Class. No.: QA927 / .A3886 2010

Dewey Class. No.: 515/.3535

Geometric analysis of hyperbolic differential equations : = an introduction /
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050 0 0 $a QA927 $b .A3886 2010
082 0 0 $a 515/.3535 $2 22
100 1 $a Alinhac, S. $q (Serge) $3 1299099
245 1 0 $a Geometric analysis of hyperbolic differential equations : $b an introduction / $c S. Alinhac.
260 # $a Cambridge, UK ; $a New York : $b Cambridge University Press, $c 2010.
300 $a ix, 118 p. ; $c 23 cm.
490 1 $a London Mathematical Society lecture note series ; $v 374
504 $a Includes bibliographical references (p. 114-116) and index.
505 0 # $a 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.
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. Hormander, 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 Hormander [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 $a Nonlinear wave equations. $3 673901
650 # 0 $a Differential equations, Hyperbolic. $3 560924
650 # 0 $a Quantum theory. $3 516552
650 # 0 $a Geometry, Differential. $3 523835
830 0 $a London Mathematical Society lecture note series ; $v 359. $3 1232938
856 4 2 $3 Cover image $u http://assets.cambridge.org/97805211/28223/cover/9780521128223.jpg