径向扩散方程源项反演的指数型正则化方法  

The Exponential Regularization Method for Source Term Inversion of Radial Diffusion Equation

作　　者：杨菲 胡彬 刘桂娟 张文 YANG Fei;HU Bin;LIU Guijuan;ZHANG Wen(School of Science,East China University of Technology,Nanchang Jiangxi 330013,China;School of Arts and Sciences,Guangzhou Maritime University,Guangzhou Guangdong 510725,China)

机构地区：[1]东华理工大学理学院,江西南昌330013 [2]广州航海学院文理学院,广东广州510725

出　　处：《江西师范大学学报(自然科学版)》2024年第5期517-523,共7页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(12261004);江西省自然科学基金重点课题(20212ACB201001);广州市教育局高校科研课题(2024312515);江西省教育厅科学技术研究课题(GJJ2200730)资助项目.

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.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.

关 键 词：径向扩散方程 源项反演 指数型正则化 时间分数阶导数 不适定问题 

分 类 号：O175.8[理学—数学]