Estimates for the characteristic problem of the first-order reduction of the wave equation

Abstract

We calculate certain estimates for the solution of the characteristic problem of the wave equation reduced to first order, in terms of the free data prescribed on two transverse surfaces, one of which is characteristic. Estimates of such kind ensure the stability of the solutions under small variations of the data. Similar estimates exist for the derivatives of the solution as well.

arXiv comment10 pages, 2 figures, to appear in J. Phys. A

References in corpus (3)

• Characteristic Evolution and Matching
• First-order quasilinear canonical representation of the characteristic formulation of the Einstein equations
• Well-posed first-order reduction of the characteristic problem of the linearized Einstein equations

Cited by in corpus (7)

• Characteristic Evolution and Matching
• Characteristic Evolution and Matching
• Well-posed first-order reduction of the characteristic problem of the linearized Einstein equations
• The Well-posedness of the Null-Timelike Boundary Problem for Quasilinear Waves
• Simulations of gravitational collapse in null coordinates: III. Hyperbolicity
• Exact boundary conditions in numerical relativity using multiple grids: scalar field tests
• Estimates for first-order homogeneous linear characteristic problems