Determining the temperature from incomplete boundary data

B. Tomas Johansson

    Research output: Contribution to journalArticlepeer-review


    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
    Issue number16
    Early online date8 Nov 2007
    Publication statusPublished - Dec 2007


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


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