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<p>This paper studies two inverse problems for the convection diffusion equation with observations at fixed times, i.e., the inverse source problem and simultaneous reconstruction of the source term and the initial condition. The statistical inversion method is applied to derive the inversion formulas, and the errors between the exact solutions and the approximations are also analyzed. Furthermore, the feasibility and effectiveness of the proposed method are verified through numerical experiments, which demonstrate that the method achieves high inversion accuracy and exhibits enhanced error tolerance.</p>

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Statistical methods for the inversion of the source term and initial values of the diffusion equation

  • 期刊论文

  • 发表日期：

    2025年7月24日

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  • Yuqian Yuan,
  • Fangfang Dou

摘要

This paper studies two inverse problems for the convection diffusion equation with observations at fixed times, i.e., the inverse source problem and simultaneous reconstruction of the source term and the initial condition. The statistical inversion method is applied to derive the inversion formulas, and the errors between the exact solutions and the approximations are also analyzed. Furthermore, the feasibility and effectiveness of the proposed method are verified through numerical experiments, which demonstrate that the method achieves high inversion accuracy and exhibits enhanced error tolerance.