A new approach to the Cauchy and Goursat problems for the nonlinear Wheeler–DeWitt equation

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Abstract

We consider a nonlinear version of the Wheeler–DeWitt equation which was introduced by Cooper, Susskind, and Thorlacius in the context of two-dimensional quantum cosmology. We establish the existence of global solutions to the Cauchy problem and Goursat problems which, both, arise naturally in physics. Our method of proof is based on a nonlinear transformation of the Wheeler–DeWitt equation and on techniques introduced by Baez and collaborators and by Tsutsumi for nonlinear wave equations.

Mathematics Subject Classification

83F05 74J30 83C47 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Center for Mathematics, Fundamental Applications, and Operations ResearchUniversidade de LisboaLisbonPortugal
  2. 2.Laboratoire Jacques-Louis Lions, Centre National de la Recherche ScientifiqueSorbonne UniversitéParisFrance

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