The Well-posedness of the Null-Timelike Boundary Problem for Quasilinear Waves
General Relativity and Quantum Cosmology
2011-06-16 v2
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.
Keywords
Cite
@article{arxiv.1010.1201,
title = {The Well-posedness of the Null-Timelike Boundary Problem for Quasilinear Waves},
author = {H-O. Kreiss and J. Winicour},
journal= {arXiv preprint arXiv:1010.1201},
year = {2011}
}
Comments
Version to appear in Class. Quantum Grav