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2009, Volume 8, Issue 1: 361-382. Doi: 10.3934/cpaa.2009.8.361
This issue Previous Article Boundary layers for the 2D linearized primitive equations Next Article A general multipurpose interpolation procedure: the magic points

Conditional Stability and Numerical Reconstruction of Initial Temperature

  • 1.

    Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T.

  • 2.

    Department of Mathematical Sciences, The University of Tokyo, Komaba Meguro Tokyo 153-8914

  • 3.

    Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

Received:  February 29, 2008
Revised:  July 31, 2008
Published:  December 2008
Abstract Related Papers Cited by
    Abstract
  • In this paper, we address an inverse problem of reconstruction of the initial temperature in a heat conductive system when some measurement data of temperature are available, which may be observed in a subregion inside or on the boundary of the physical domain, along a time period which may start at some point, possibly far away from the initial time. A conditional stability estimate is first achieved by the Carleman estimate for such reconstruction. Numerical reconstruction algorithm is proposed based on the output least-squares formulation with the Tikhonov regularization using the finite element discretization, and the existence and convergence of the finite element solution are presented. Numerical experiments are carried out to demonstrate the applicability and effectiveness of the proposed method.
    Mathematics Subject Classification: Primary: 65N30; Secondary: 35R30.

    Citation:
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