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

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.

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Correspondence to Philippe G. LeFloch.

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Dias, J., LeFloch, P.G. A new approach to the Cauchy and Goursat problems for the nonlinear Wheeler–DeWitt equation. Nonlinear Differ. Equ. Appl. 25, 10 (2018). https://doi.org/10.1007/s00030-018-0503-0

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Mathematics Subject Classification

  • 83F05
  • 74J30
  • 83C47