On the characteristic initial value problem for nonlinear symmetric hyperbolic systems, including Einstein equations

2014/06/11 by Aurore Cabet, Piotr T. Chruściel, Cabet, Aurore +3
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Waves and Solitons #Stability and Controllability of Differential Equations #gr-qc #math.AP

paper · pdf · doi:10.48550/arxiv.1406.3009

85 pages, 11 figures

arxiv created 2016/03/26 · arxiv updated 2016/03/29

Abstract

We consider a characteristic initial value problem for a class of symmetric hyperbolic systems with initial data given on two smooth null intersecting characteristic surfaces. We prove existence of solutions on a future neighborhood of the initial surfaces. The general result is applied to general semilinear wave equations, as well as the Einstein equations with or without sources, and conformal variations thereof.

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