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A Revised Tikhonov Regularization Method for a Cauchy Problem of Two-Dimensional Heat Conduction Equation

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  • Songshu Liu
  • Lixin Feng

Abstract

In this paper we investigate a Cauchy problem of two-dimensional (2D) heat conduction equation, which determines the internal surface temperature distribution from measured data at the fixed location. In general, this problem is ill-posed in the sense of Hadamard. We propose a revised Tikhonov regularization method to deal with this ill-posed problem and obtain the convergence estimate between the approximate solution and the exact one by choosing a suitable regularization parameter. A numerical example shows that the proposed method works well.

Suggested Citation

  • Songshu Liu & Lixin Feng, 2018. "A Revised Tikhonov Regularization Method for a Cauchy Problem of Two-Dimensional Heat Conduction Equation," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-8, May.
    • Handle: RePEc:hin:jnlmpe:1216357
    DOI: 10.1155/2018/1216357
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    Cited by:

    1. Yonggang Chen & Yu Qiao & Xiangtuan Xiong, 2022. "Regularization Error Analysis for a Sideways Problem of the 2D Nonhomogeneous Time-Fractional Diffusion Equation," Mathematics, MDPI, vol. 10(10), pages 1-14, May.

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