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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.
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N. T. Bishop, R. Gómez, L. Lehner, B. Szilágyi, J. Winicour and R. A. Isaacson, “Cauchy-Characteristic Matching”, in B Iyer and B Bhawal (Eds.), Black Holes, Gravitational Radiation and the Universe
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