Local existence of a solution of a semi-linear wave equation in a neighborhood of initial characteristic hypersurfaces
On the characteristic initial value problem for nonlinear symmetric hyperbolic systems, including Einstein equations
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.
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