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arXiv · 1010.1201

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

H-O. Kreiss·J. Winicour
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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.

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H-O. Kreiss, J. Winicour. 2011-05-17. The Well-posedness of the Null-Timelike Boundary Problem for Quasilinear Waves. https://doi.org/10.1088/0264-9381%2F28%2F14%2F145020

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