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

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

2010-10-06

arxiv.org/abs/1010.1201v2

Class.Quant.Grav.28:145020,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Version to appear in Class. Quantum Grav

Scientific paper

10.1088/0264-9381/28/14/145020

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.

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