عنوان

Geometric analysis of hyperbolic differential equations :

(Number (ISBN

0521128226 (pbk.)

(Number (ISBN

9780521128223 (pbk.)

Number

dltt

Title Proper

Geometric analysis of hyperbolic differential equations :

General Material Designation

[Book]

Other Title Information

an introduction /

First Statement of Responsibility

S. Alinhac

Place of Publication, Distribution, etc.

New York :

Name of Publisher, Distributor, etc.

Cambridge University Press,

Date of Publication, Distribution, etc.

2010

Specific Material Designation and Extent of Item

ix, 118 p. ;

Dimensions

23 cm

Series Title

London Mathematical Society lecture note series ;

Volume Designation

374

Text of Note

Includes bibliographical references and index

Text of Note

Machine generated contents note: 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

8

Text of Note

"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

Text of Note

"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

Differential equations, Hyperbolic

Geometry, Differential

Nonlinear wave equations

Quantum theory

Number

Edition

Class number

Book number

Alinhac, S., (Serge)

Date of Transaction

20100819115306.0

Electronic name

[Book]

Y