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

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.

arXiv commentVersion to appear in Class. Quantum Grav

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Cited by in corpus (7)

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• Boundary Conditions for the Gravitational Field
• Testing the well-posedness of characteristic evolution of scalar waves