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General Relativity and the Einstein Equations$
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Yvonne Choquet-Bruhat

Print publication date: 2008

Print ISBN-13: 9780199230723

Published to Oxford Scholarship Online: May 2009

DOI: 10.1093/acprof:oso/9780199230723.001.0001

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Other Hyperbolic-Elliptic Well-Posed Systems

Other Hyperbolic-Elliptic Well-Posed Systems

Chapter:
(p.238) VIII Other Hyperbolic-Elliptic Well-Posed Systems
Source:
General Relativity and the Einstein Equations
Author(s):

Yvonne Choquet-Bruhat

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199230723.003.0008

This chapter presents well-posed hyperbolic or hyperbolic-elliptic systems that lead to the same local existence andgeometric uniqueness theorems as the wave gauge choice. However, these different formulations may be important in numerical studies or global existence proofs. Topics covered include Leray–Ohya non-hyperbolicity of Rij = 0, wave equation for K, fourth-order non-strict and strict hyperbolic systems, first-order hyperbolic systems, Bianchi–Einstein equations, Bel–Robinson tensor and energy, and Bel–Robinson energy in a strip.

Keywords:   hyperbolic systems, Leray–Ohya non-hyperbolicity, wave equation, Bianchi–Einstein equations, Bel–Robinson energy

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