Determining the temperature from incomplete boundary data

B. Tomas Johansson

Research output: Contribution to journalArticle

Abstract

An iterative procedure for determining temperature fields from Cauchy data given on a part of the boundary is presented. At each iteration step, a series of mixed well-posed boundary value problems are solved for the heat operator and its adjoint. A convergence proof of this method in a weighted L2-space is included, as well as a stopping criteria for the case of noisy data. Moreover, a solvability result in a weighted Sobolev space for a parabolic initial boundary value problem of second order with mixed boundary conditions is presented. Regularity of the solution is proved. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Original languageEnglish
Pages (from-to)1765-1779
Number of pages15
JournalMathematische Nachrichten
Volume280
Issue number16
Early online date8 Nov 2007
DOIs
Publication statusPublished - Dec 2007

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Stopping Criterion
Weighted Sobolev Spaces
Mixed Boundary Conditions
Noisy Data
Weighted Spaces
Iterative Procedure
Parabolic Problems
Temperature Field
Initial-boundary-value Problem
Cauchy
Solvability
Heat
Regularity
Boundary Value Problem
Iteration
Series
Operator

Keywords

  • Cauchy problem
  • heat equation
  • ill-posed
  • iterative regularization
  • weighted Sobolev space

Cite this

Johansson, B. Tomas. / Determining the temperature from incomplete boundary data. In: Mathematische Nachrichten. 2007 ; Vol. 280, No. 16. pp. 1765-1779.
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Determining the temperature from incomplete boundary data. / Johansson, B. Tomas.

In: Mathematische Nachrichten, Vol. 280, No. 16, 12.2007, p. 1765-1779.

Research output: Contribution to journalArticle

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