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          Institute: MPI für Gravitationsphysik     Collection: Astrophysical Relativity     Display Documents



  history
ID: 441599.0, MPI für Gravitationsphysik / Astrophysical Relativity
Boundary conditions for coupled quasilinear wave equations with application to isolated systems
Authors:Kreiss, H.-O.; Reula, O.; Sarbach, O.; Winicour, J.
Date of Publication (YYYY-MM-DD):2009
Title of Journal:Communications in Mathematical Physics
Volume:289
Issue / Number:3
Start Page:1099
End Page:1129
Review Status:not specified
Audience:Not Specified
Abstract / Description:We consider the initial-boundary value problem for systems of quasilinear wave equations on domains of the form $[0,T] \times \Sigma$, where $\Sigma$ is a compact manifold with smooth boundaries $\partial\Sigma$. By using an appropriate reduction to a first order symmetric hyperbolic system with maximal dissipative boundary conditions, well posedness of such problems is established for a large class of boundary conditions on $\partial\Sigma$. We show that our class of boundary conditions is sufficiently general to allow for a well posed formulation for different wave problems in the presence of constraints and artificial, nonreflecting boundaries, including Maxwell's equations in the Lorentz gauge and Einstein's gravitational equations in harmonic coordinates. Our results should also be useful for obtaining stable finite-difference discretizations for such problems.
External Publication Status:published
Document Type:Article
Communicated by:Bernhard F. Schutz
Affiliations:MPI für Gravitationsphysik/Astrophysical Relativity
Identifiers:DOI:10.1007/s00220-009-0788-2
LOCALID:arXiv:0807.3207
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