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.
@book{bwmeta1.element.bwnjournal-rm-doi-10_4064-dm732-7-2015,
author = {Aurore Cabet and Piotr T. Chru\'sciel and Roger Tagne Wafo},
title = {On the characteristic initial value problem for nonlinear symmetric hyperbolic systems, including Einstein equations},
series = {GDML\_Books},
year = {2016},
zbl = {06602795},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm732-7-2015}
}
Aurore Cabet; Piotr T. Chruściel; Roger Tagne Wafo. On the characteristic initial value problem for nonlinear symmetric hyperbolic systems, including Einstein equations. GDML_Books (2016), http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm732-7-2015/