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In this article we summarize what is known about the initial-boundary value problem for general relativity and discuss present problems related to it.
Reading the bibliography…
In this article we summarize what is known about the initial-boundary value problem for general relativity and discuss present problems related to it.
Reading the bibliography…
Théorème d’existence pour certains systèmes d’équations aux dérivées partielles non linéaires
Y. Fourès-Bruhat · 1951
Earlier work this paper cites.
Symmetric positive linear differential equations
K.O. Friedrichs · 1958
Earlier work this paper cites.
Local boundary conditions for dissipative symmetric linear differential operators
P.D. Lax and R.S. Phillips · 1960
Earlier work this paper cites.
Global aspects of the Cauchy problem in general relativity
Y. Choquet-Bruhat and R. Geroch · 1969
Earlier work this paper cites.
Initial boundary value problems for hyperbolic systems
H.O. Kreiss · 1970
Earlier work this paper cites.
Absorbing boundary conditions for the numerical simulation of waves
B. Engquist and A. Majda · 1977
Earlier work this paper cites.
Initial-Boundary Value Problems and the Navier-Stokes Equations
H.O. Kreiss and J. Lorenz · 1989
Earlier work this paper cites.
Time dependent problems and difference methods
B. Gustafsson, H. Kreiss, and J. Oliger · 1995
Earlier work this paper cites.
Evolution of three-dimensional gravitational waves: Harmonic slicing case
M. Shibata and T. Nakamura · 1995
Earlier work this paper cites.
Partial differential equations of physics
R Geroch · 1996
Earlier work this paper cites.
Hyperbolic methods for Einstein’s equations
O.A. Reula · 1998
Earlier work this paper cites.
On the numerical integration of Einstein’s field equations
T.W. Baumgarte and S.L. Shapiro · 1998
Cited alongside, same era.
The initial boundary value problem for Einstein’s vacuum field equations
H. Friedrich and G. Nagy · 1999
Cited alongside, same era.
Some mathematical questions connected with first and second order time-dependent systems of partial differential equations
H.O. Kreiss and O.E. Ortiz · 2002
Cited alongside, same era.
Hyperbolicity of the baumgarte-shapiro-shibata-nakamura system of Einstein evolution equations
O. Sarbach, G. Calabrese, J. Pullin, and M. Tiglio · 2002
Cited alongside, same era.
Well-posed initial-boundary evolution in general relativity
B. Szilagyi and J. Winicour · 2003
Cited alongside, same era.
Well posed constraint-preserving boundary conditions for the linearized Einstein equations
G. Calabrese, J. Pullin, O. Reula, O. Sarbach, and M. Tiglio · 2003
Cited alongside, same era.
Strongly hyperbolic second order Einstein’s evolution equations
G. Nagy, O.E. Ortiz, and O.A. Reula · 2004
Cited alongside, same era.
Strongly hyperbolic systems in general relativity
O.A. Reula · 2004
Cited alongside, same era.
On the well posedness of the Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein’s field equations
H. Beyer and O. Sarbach · 2004
Cited alongside, same era.
Problems which are well-posed in a generalized sense with applications to the Einstein equations
H.O. Kreiss and J. Winicour · 2006
Cited alongside, same era.
A new generalized harmonic evolution system
L. Lindblom, M.A. Scheel, L.E. Kidder, R. Owen, and O. Rinne · 2006
Cited alongside, same era.
Towards absorbing outer boundaries in general relativity
L.T. Buchman and O.C.A. Sarbach · 2006
Later among the works it cites.
Absorbing boundary conditions for Einstein’s field equations
O. Sarbach · 2006
Later among the works it cites.
Well-posed initial-boundary value problem for the harmonic Einstein equations using energy estimates
H.O. Kreiss, O. Reula, O. Sarbach, and J. Winicour · 2007
Later among the works it cites.
Outer boundary conditions for Einstein’s field equations in harmonic coordinates
M. Ruiz, O. Rinne, and O. Sarbach · 2007
Later among the works it cites.
Testing outer boundary treatments for the Einstein equations
O. Rinne, L. Lindblom, and M.A. Scheel · 2007
Later among the works it cites.
Boundary conditions for coupled quasilinear wave equations with applications to isolated systems
H.O. Kreiss, O. Reula, O. Sarbach, and J. Winicour · 2009
Later among the works it cites.
Geometrization of metric boundary data for Einstein’s equations
J. Winicour · 2009
Later among the works it cites.
Disembodied boundary data for Einstein’s equations
J. Winicour · 2009
Later among the works it cites.
Initial boundary value problems for Einstein’s field equations and geometric uniqueness
H. Friedrich · 2009
Later among the works it cites.
D. Núñez and O. Sarbach · 2010
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