An iterative method for a Cauchy problem for the heat equation

Tomas Johansson

Research output: Contribution to journalArticle

Abstract

An iterative method for reconstruction of the solution to a parabolic initial boundary value problem of second order from Cauchy data is presented. The data are given on a part of the boundary. At each iteration step, a series of well-posed mixed boundary value problems are solved for the parabolic operator and its adjoint. The convergence proof of this method in a weighted L2-space is included.

Original languageEnglish
Pages (from-to)262-286
Number of pages25
JournalIMA Journal of Applied Mathematics
Volume71
Issue number2
Early online date10 Jun 2005
DOIs
Publication statusPublished - Apr 2006

Keywords

  • cauchy problem
  • heat equation
  • iterative regularization method
  • mixed problem
  • weighted Sobolev space

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