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

Volume 515 / 2016

Aurore Cabet, Piotr T. Chruściel, Roger Tagne Wafo 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.

Authors

  • Aurore CabetDépartement d’Informatique
    Université de Tours
    41000 Blois, France
    e-mail
  • Piotr T. ChruścielFaculty of Physics and Erwin Schrödinger Institute
    Universität Wien
    1090 Wien, Austria
    homepage.univie.ac.at/piotr.chrusciel
    e-mail
  • Roger Tagne WafoDepartment of Mathematics and Computer Science
    Faculty of Science
    University of Douala
    P.O. Box 24157, Douala, Cameroon
    e-mail

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