【摘要】 该文主要研究径向扩散方程的源项反演问题，在分析了反源问题的不适定性和条件稳定性的基础上给出了源项反演的指数型正则化方法.然后，对于先验选取和后验选取正则化参数，分别给出了径向扩散方程源项的正则化解的收敛性.数值实验结果表明：新的指数型正则化方法能有效地实现源项的反演，且对于噪声强度较大的测量数据也能获得令人满意的反演结果.更多还原

【Abstract】 The source term inversion problem of the radial diffusion equation is mainly studied in this paper.Based on analysis of the ill-posedness and conditional stability of the inverse source problem, the exponential regularization method for the source term inversion is proposed.Then, for the cases of prior selection and posterior selection of regularization parameters, the convergence of regularization solutions of the source term in the radial diffusion equation is given, respectively.The numerical experimental results show that the exponential regularization method proposed in this paper can effectively achieve the inversion of source term, and satisfactory inversion results can also be obtained for measurement data with high noise level.更多还原