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Journal Article

The Well-posedness of the Null-Timelike Boundary Problem for Quasilinear Waves

MPS-Authors

Kreiss,  H-O.
AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

Winicour,  J.
AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

1010.1201.pdf
(Preprint), 329KB

CQG_28_14_145020.pdf
(Any fulltext), 191KB

Supplementary Material (public)
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Citation

Kreiss, H.-O., & Winicour, J. (2011). The Well-posedness of the Null-Timelike Boundary Problem for Quasilinear Waves. Classical and quantum gravity, 28(14): 145020. doi:10.1088/0264-9381/28/14/145020.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-06AA-F
Abstract
The null-timelike initial-boundary value problem for a hyperbolic system of equations consists of the evolution of data given on an initial characteristic surface and on a timelike worldtube to produce a solution in the exterior of the worldtube. We establish the well-posedness of this problem for the evolution of a quasilinear scalar wave by means of energy estimates. The treatment is given in characteristic coordinates and thus provides a guide for developing stable finite difference algorithms. A new technique underlying the approach has potential application to other characteristic initial-boundary value problems.