% $PublicationNumber:lrr-1998-3$
% $BibSchema:new$
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author = {Bruhat, Y.},
format = {print},
journal = {Acta Math.},
keywords = {Existence theorems, Initial value problem, Uniqueness theorems},
pages = {141--225},
title = {Th\'eor\`eme d'existence pour certains syst\`emes d'\'equations aux d\'eriv\'ees partielles non lin\'eaires},
volume = {88},
year = {1952}
}
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author = {Hughes, T. and Kato, T. and Marsden, J.},
format = {print},
journal = {Arch. Ration. Mech. Anal.},
keywords = {Existence theorems, Hyperbolic equations, Initial value problem, Uniqueness theorems},
pages = {273--294},
title = {Well-posed quasi-linear second order hyperbolic systems with applications to nonlinear elastodynamics and general relativity},
volume = {63},
year = {1976}
}
@article{C-BCF,
author = {Choquet-Bruhat, Y. and Christodoulou, D. and Francaviglia, M.},
format = {print},
journal = {Ann. Inst. Henri Poincare A},
keywords = {Existence theorems, Hyperbolic equations, Initial value problem, Uniqueness theorems},
pages = {241--255},
title = {Cauchy data on a manifold},
volume = {29},
year = {1978}
}
@article{C-B68,
author = {Choquet-Bruhat, Y.},
format = {print},
journal = {Ann. Inst. Henri Poincare},
keywords = {Existence theorems, Hyperbolic equations, Initial value problem, Uniqueness theorems},
pages = {327--338},
title = {Espaces temps eineiniens g\'en\'eraux, chocs gravitationnels},
volume = {8},
year = {1968}
}
@book{HE,
address = {Cambridge},
author = {Hawking, S.W. and Ellis, G.F.R.},
format = {print},
keywords = {General relativity, Initial value problem},
publisher = {Cambridge University Press},
series = {Cambridge Monographs on Mathematical Physics},
title = {The Large Scale Structure of Space-Time},
year = {1973}
}
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author = {Fischer, A. and Marsden, J.},
format = {print},
journal = {Commun. Math. Phys.},
keywords = {Existence theorems, Hyperbolic equations, Initial value problem, Uniqueness theorems},
pages = {1--38},
title = {The Einstein Evolution Equations as a First-Order Symmetric Hyperbolic Quasilinear System},
volume = {28},
year = {1972}
}
@inproceedings{FM73,
address = {Providence},
author = {Fischer, A. and Marsden, J.},
booktitle = {Partial Differential Equations},
editor = {Spencer, D.C.},
format = {print},
keywords = {Existence theorems, Hyperbolic equations, Initial value problem, Uniqueness theorems},
pages = {309--327},
publisher = {AMS},
series = {Proceedings of Symposia in Pure Mathematics},
title = {General relativity, partial differential equations, and dynamical systems},
volume = {23},
year = {1973}
}
@article{C-BC,
author = {Choquet-Bruhat, Y. and Christodoulou, D.},
format = {print},
journal = {Acta Math.},
keywords = {Elliptic equations, Functional analysis},
pages = {129--150},
title = {Elliptic systems in $H_{s,\delta}$ spaces on manifolds which are Euclidean at infinity},
volume = {145},
year = {1981}
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author = {Christodoulou, D. and {\'{O}} Murchadha, N.},
format = {print},
journal = {Commun. Math. Phys.},
keywords = {Existence theorems, Initial value problem, Uniqueness theorems},
pages = {271--300},
title = {The boost problem in general relativity},
volume = {80},
year = {1981}
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author = {Geroch, R.},
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keywords = {Existence theorems, Initial value problem, Uniqueness theorems},
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pages = {1851--1858},
title = {The Local Nonsingularity Theorem},
volume = {24},
year = {1983}
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author = {Geroch, R. and Xanthopolous, B.C.},
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keywords = {Asymptotics, Stability theory},
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title = {Asymptotic Simplicity Is Stable},
volume = {19},
year = {1978}
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@article{Frie81-1,
adsurl = {http://adsabs.harvard.edu/abs/1981RSPSA.375..169F},
author = {Friedrich, H.},
format = {print},
journal = {Proc. R. Soc. London, Ser. A},
keywords = {Asymptotics, Existence theorems, Hyperbolic equations, Initial value problem, Uniqueness theorems},
pages = {169--184},
title = {On the regular and the asymptotic characteristic initial value problem for Einstein's vacuum field equations},
volume = {375},
year = {1981}
}
@article{Frie81-2,
adsurl = {http://adsabs.harvard.edu/abs/1981RSPSA.378..401F},
author = {Friedrich, H.},
doi = {10.1098/rspa.1981.0159},
format = {print},
journal = {Proc. R. Soc. London, Ser. A},
keywords = {Asymptotics, Existence theorems, Hyperbolic equations, Initial value problem, Uniqueness theorems},
pages = {401--421},
title = {The Asymptotic Characteristic Initial Value Problem for Einstein's Vacuum Field Equations as an Initial Value Problem for a First-Order Quasilinear Symmetric Hyperbolic System},
volume = {378},
year = {1981}
}
@article{CW,
author = {Cutler, C. and Wald, R.M.},
format = {print},
journal = {Class. Quantum Grav.},
keywords = {Asymptotics, Existence theorems, Hyperbolic equations, Initial value problem, Uniqueness theorems},
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title = {Existence of radiating Einstein--Maxwell solutions which are $C^\infty$ on all of $I^-$ and $I^+$},
volume = {6},
year = {1989}
}
@book{CK,
address = {Princeton},
author = {Christodoulou, D. and Klainerman, S.},
format = {print},
keywords = {Asymptotics, Existence theorems, Hyperbolic equations, Initial value problem, Uniqueness theorems},
publisher = {Princeton University Press},
series = {Princeton Mathematical Series},
title = {The Global Nonlinear Stability of the Minkowski Space},
volume = {41},
year = {1993}
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author = {Klainerman, S.},
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keywords = {Existence theorems, Global solutions, Hyperbolic equations, Initial value problem, Uniqueness theorems},
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title = {The null condition and global existence to nonlinear wave equations},
volume = {23},
year = {1986}
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keywords = {Existence theorems, Global solutions, Hyperbolic equations, Initial value problem, Uniqueness theorems},
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title = {Remarks on the global Sobolev inequalities in Minkowski Space},
volume = {40},
year = {1987}
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keywords = {Existence theorems, Global solutions, Hyperbolic equations, Initial value problem, Uniqueness theorems},
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volume = {38},
year = {1985}
}
@preprint{G,
author = {Geroch, R.},
eprint = {gr-qc/9602055},
format = {arxiv},
keywords = {Differential equations},
note = {Scottish Summer School in Theoretical Physics},
title = {Partial Differential Equations of Physics},
year = {1996}
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@book{KL,
address = {Boston},
author = {Kreiss, H.-O. and Lorentz, J.},
format = {print},
keywords = {Differential equations, Fluid dynamics, Initial value problem},
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title = {Initial-Boundary Value Problems and the Navier--Stokes Equations},
volume = {136},
year = {1989}
}
@book{GKO,
address = {New York},
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keywords = {Differential equations, Initial value problem, Numerical methods},
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title = {Time Dependent Problems and Difference Methods},
year = {1995}
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@book{TAYLOR-NLPDE,
address = {Boston},
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format = {print},
keywords = {Differential equations, Initial value problem},
publisher = {Birkh\"{a}user},
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title = {Pseudodifferential Operators and Nonlinear PDE},
volume = {100},
year = {1991}
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@book{HADA,
address = {New Haven},
author = {Hadamard, J.},
format = {print},
keywords = {Differential equations, Initial value problem},
publisher = {Yale University Press},
title = {Lectures on Cauchy's Problem in Linear Partial Differential Equations},
year = {1923}
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author = {Kreiss, H.-O.},
format = {print},
journal = {Math. Scand.},
keywords = {Differential equations, Initial value problem},
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title = {\"Uber sachgem\"asse Cauchyprobleme},
volume = {7},
year = {1959}
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@book{Leray,
address = {Princeton},
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title = {Hyperbolic Differential Equations},
year = {1953}
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author = {Leray, J. and Ohya, Y.},
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@inproceedings{J,
address = {Berlin},
author = {John, F.},
booktitle = {Trends and Applications of Pure Mathematics to Mechanics},
conference = {Invited and Contributed Papers presented at a Symposium at \'Ecole Polytechnique, Palaiseau, France, November 28\,--\,December 2, 1983},
editor = {Ciarlet, P.G. and Roseau, M.},
format = {print},
keywords = {Differential equations, Genuinely nonlinear equations, Initial value problem, Shock waves, Singularities},
pages = {194--210},
publisher = {Springer},
series = {Lecture Notes in Physics},
title = {Formation of Singularities in Elastic Waves},
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keywords = {Differential equations, Genuinely nonlinear equations, Initial value problem, Shock waves, Singularities},
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year = {1985}
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@article{KNOR97,
adsurl = {http://adsabs.harvard.edu/abs/1997JMP....38.5272K},
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keywords = {Differential equations, Fluid dynamics, Hyperbolic equations, Initial value problem, Stability theory},
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year = {1997}
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@book{W,
address = {Chicago},
author = {Wald, R.M.},
format = {print},
keywords = {General relativity},
publisher = {University of Chicago Press},
title = {General Relativity},
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@article{Bruhat73,
author = {Bruhat, Y.},
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journal = {C. R. Acad. Sci.},
keywords = {Gauge conditions, Initial value problem, Stability theory},
pages = {281},
title = {Un th\'eor\`eme d'inestabilit\'e pour certain \'equations hyperboliques nonlin\'eaires},
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year = {1973}
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author = {Alcubierre, M.},
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author = {Friedrich, H.},
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@article{Frie96,
adsurl = {http://adsabs.harvard.edu/abs/1996CQGra..13.1451F},
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journal = {Class. Quantum Grav.},
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year = {1996}
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year = {1983}
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@article{CBR83,
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keywords = {ADM formalism, Existence theorems, Gauge conditions, Hyperbolic equations, Initial value problem, Uniqueness theorems},
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volume = {89},
year = {1983}
}
@article{AACBY95,
author = {Abrahams, A.M. and Anderson, A. and Choquet-Bruhat, Y. and York Jr, J.W.},
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keywords = {ADM formalism, Existence theorems, Gauge conditions, Hyperbolic equations, Initial value problem, Uniqueness theorems},
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volume = {75},
year = {1996}
}
@article{AACBY971,
author = {Abrahams, A.M. and Anderson, A. and Choquet-Bruhat, Y. and York Jr, J.W.},
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volume = {14},
year = {1997}
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author = {Abrahams, A.M. and Anderson, A. and Choquet-Bruhat, Y. and York Jr, J.W.},
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format = {arxiv},
keywords = {ADM formalism, Existence theorems, Gauge conditions, Hyperbolic equations, Initial value problem, Uniqueness theorems},
title = {Hyperbolic Formulation of General Relativity},
year = {1997}
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year = {1992}
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keywords = {ADM formalism, Existence theorems, Gauge conditions, Hyperbolic equations, Initial value problem, Uniqueness theorems},
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year = {1995}
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year = {1997}
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keywords = {ADM formalism, Existence theorems, Harmonic gauge, Hyperbolic systems, Initial value problem, Newtonian limit, Uniqueness theorems},
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year = {1994}
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volume = {76},
year = {1996}
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year = {1996}
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author = {Ashtekar, A.},
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@book{Ash88,
address = {Naples},
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@article{ILR97,
author = {Iriondo, M.S. and Leguizam{\'{o}}n, E.O. and Reula, O.A.},
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keywords = {Ashtekar variables},
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title = {Einstein's equations in Ashtekar variables constitute a symmetric hyperbolic system},
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@article{AM97,
author = {Alcubierre, M. and Mass{\'{o}}, J.},
eprint = {gr-qc/9709024},
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keywords = {ADM formalism, Gauge conditions, Hyperbolic equations, Initial value problem},
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title = {Pathologies of hyperbolic gauges in general relativity and other field theories},
volume = {57},
year = {1998}
}
@inproceedings{CBY962,
address = {Bologna},
author = {Choquet-Bruhat, Y. and York Jr, J.W.},
booktitle = {Gravitation, Electromagnetism and Geometric Structures},
conference = {International Conference in honour of A. Lichnerowicz, Villa Tuscolana, 19\,--\,23 October 1995},
editor = {Ferrarese, G.},
eprint = {gr-qc/9601030},
format = {print},
keywords = {ADM formalism, Elliptic equations, Existence theorems, Gauge conditions, Hyperbolic equations, Initial value problem, Mixed systems, Uniqueness theorems},
publisher = {Pitagora},
title = {Mixed elliptic and hyperbolic system for the Einstein equations},
year = {1996}
}
@article{AACBY96,
author = {Abrahams, A. and Anderson, A. and Choquet-Bruhat, Y. and York Jr, J.W.},
eprint = {gr-qc/9607006},
format = {print},
journal = {C. R. Acad. Sci. Ser. II},
keywords = {ADM formalism, Existence theorems, Gauge conditions, Hyperbolic equations, Initial value problem, Uniqueness theorems},
pages = {835--841},
title = {A nonstrictly hyperbolic system for the Einstein equations with arbitrary lapse and shift},
volume = {323},
year = {1996}
}
@article{Rendall,
author = {Rendall, A.D.},
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keywords = {ADM formalism, Hyperbolic equations, Initial value problem, Newtonian limit},
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title = {The Newtonian limit for asymptotically flat solutions of the Vlasov--Einstein system},
volume = {163},
year = {1994}
}
@article{FR97,
author = {Frittelli, S.},
format = {print},
journal = {Phys. Rev. D},
keywords = {ADM formalism, Existence theorems, Hyperbolic equations, Initial value problem, Uniqueness theorems},
pages = {5992--5996},
title = {Note on the propagation of the constraints in standard 3+1 general relativity},
volume = {55},
year = {1997}
}
@article{ILR-NL,
author = {Iriondo, M.S. and Leguizam{\'{o}}n, E.O. and Reula, O.A.},
eprint = {gr-qc/9709078},
format = {print},
journal = {J. Math. Phys.},
keywords = {ADM formalism, Existence theorems, Hyperbolic equations, Initial value problem, Newtonian limit, Radiation, Slow solutions, Uniqueness theorems},
pages = {1555--1565},
title = {Fast and slow solutions in General Relativity: The initialization procedure},
volume = {39},
year = {1998}
}
@preprint{ILR-NNL,
author = {Iriondo, M.S. and Leguizam{\'{o}}n, E.O. and Reula, O.A.},
eprint = {gr-qc/9710003},
format = {arxiv},
keywords = {Asymptotics, Existence theorems, Hyperbolic equations, Initial value problem, Newtonian limit, Radiation, Slow solutions, Uniqueness theorems},
title = {The Newtonian Limit on Asymptotically Null Foliations},
year = {1997}
}