On determinism and well-posedness in multiple time dimensions

  title={On determinism and well-posedness in multiple time dimensions},
  author={Walter Craig and Steven Weinstein},
  journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
  pages={3023 - 3046}
  • W. Craig, Steven Weinstein
  • Published 1 December 2008
  • Mathematics
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
We study the initial value problem for the wave equation and the ultrahyperbolic equation for data posed on initial hypersurfaces surface of arbitrary space–time signature. We show that, under a non-local constraint, the initial value problem posed on codimension-one hypersurfaces—the Cauchy problem—has global unique solutions in the Sobolev spaces Hm. Thus, it is well-posed. However, we show that the initial value problem on higher codimension hypersurfaces is ill-posed due to failure of… 
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