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<p>In this paper, we investigate a backward heat conduction problem for a complete parabolic equation in <i>n</i>-dimensional space. Based on the Fourier transform technique, the problem is solved and it is recognized that this problem is seriously ill-posed. We adopt the modified Tikhonov regularization method to solve this inverse problem. Under an a-priori and an a-posteriori regularization parameter choice rules, the Hölder type error estimates of the exact solution and the regularization solution are derived. Furthermore, the convergence estimation for the regularization solution at initial moment is solved by improving the a-priori bound smoothness condition. Finally, numerical examples are presented to verify the effectiveness and stability of this regularization approach.</p>

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The modified Tikhonov regularization method for backward heat conduction problem with a complete parabolic equation in \({{\mathbb {R}}^{n}}\)

  • 期刊论文

  • 发表日期：

    2025年7月16日

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  • Wen-Qiong Hou,
  • Fan Yang,
  • Xiao-Xiao Li,
  • Zhen-Ji Tian

摘要

In this paper, we investigate a backward heat conduction problem for a complete parabolic equation in n-dimensional space. Based on the Fourier transform technique, the problem is solved and it is recognized that this problem is seriously ill-posed. We adopt the modified Tikhonov regularization method to solve this inverse problem. Under an a-priori and an a-posteriori regularization parameter choice rules, the Hölder type error estimates of the exact solution and the regularization solution are derived. Furthermore, the convergence estimation for the regularization solution at initial moment is solved by improving the a-priori bound smoothness condition. Finally, numerical examples are presented to verify the effectiveness and stability of this regularization approach.