Well-posed two-point initial-boundary value problems with arbitrary boundary conditions

@article{Smith2011WellposedTI,
  title={Well-posed two-point initial-boundary value problems with arbitrary boundary conditions},
  author={David A. Smith},
  journal={Mathematical Proceedings of the Cambridge Philosophical Society},
  year={2011},
  volume={152},
  pages={473 - 496}
}
  • David A. Smith
  • Published 29 April 2011
  • Mathematics
  • Mathematical Proceedings of the Cambridge Philosophical Society
Abstract We study initial-boundary value problems for linear evolution equations of arbitrary spatial order, subject to arbitrary linear boundary conditions and posed on a rectangular 1-space, 1-time domain. We give a new characterisation of the boundary conditions that specify well-posed problems using Fokas' transform method. We also give a sufficient condition guaranteeing that the solution can be represented using a series. The relevant condition, the analyticity at infinity of certain… 
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