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

Kreiss, H-O.; Winicour, J.

doi:10.1088/0264-9381/28/14/145020

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

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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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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: https://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.