Geometric analysis of hyperbolic differential equations : an introduction

Resource Information

The work Geometric analysis of hyperbolic differential equations : an introduction represents a distinct intellectual or artistic creation found in University of Missouri Libraries. This resource is a combination of several types including: Work, Language Material, Books.

Label

Geometric analysis of hyperbolic differential equations : an introduction

Title remainder

an introduction

Statement of responsibility

S. Alinhac

Creator

• Alinhac, S., (Serge)

Subject

• Differential equations, Hyperbolic
• Geometry, Differential
• Nonlinear wave equations
• Quantum theory

Language

eng

Summary

• "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

Member of

• London Mathematical Society lecture note series, 374

Cataloging source

DLC

Dewey number

515/.3535

Index

index present

LC call number

QA927

LC item number

.A3886 2010

Literary form

non fiction

Nature of contents

bibliography

Series statement

London Mathematical Society lecture note series

Series volume

374