Well-Posed Initial-Boundary Value Problem for a Constrained Evolution System and Radiation-Controlling Constraint-Preserving Boundary Conditions

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dc.creatorAlekseenko, Alexander M.
dc.date2006-11-02
dc.date2007-08-23
dc.date.accessioned2026-07-07T08:25:03Z
dc.date.available2026-07-07T08:25:03Z
dc.descriptionA well-posed initial-boundary value problem is formulated for the model problem of the vector wave equation subject to the divergence-free constraint. Existence, uniqueness and stability of the solution is proved by reduction to a system evolving the constraint quantity statically, i.e., the second time derivative of the constraint quantity is zero. A new set of radiation-controlling constraint-preserving boundary conditions is constructed for the free evolution problem. Comparison between the new conditions and the standard constraint-preserving boundary conditions is made using the Fourier-Laplace analysis and the power series decomposition in time. The new boundary conditions satisfy the Kreiss condition and are free from the ill-posed modes growing polynomially in time.
dc.descriptionTo appear in the Journal of Hyperbolic Differential Equations. In response to the reviewers request, a theorem on well-posedness of the free evolution problem has been added, definitions clarified in Sections 4 and 5, as well as a typo was removed from Section 6
dc.identifierhttps://arxiv.org/abs/gr-qc/0611011
dc.identifierhttp://arxiv.org/abs/gr-qc/0611011
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/136545
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleWell-Posed Initial-Boundary Value Problem for a Constrained Evolution System and Radiation-Controlling Constraint-Preserving Boundary Conditions
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