On the characteristic initial value problem for nonlinear symmetric hyperbolic systems, including Einstein equations
Volume 515 / 2016
Dissertationes Mathematicae 515 (2016), 1-67
MSC: Primary 35L45; Secondary 35L52, 58J45, 83C05.
DOI: 10.4064/dm732-7-2015
Published online: 18 March 2016
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 result is applied to general semilinear wave equations, as well as the Einstein equations with or without sources, and conformal variations thereof.
