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《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (6): 64-73.doi: 10.6040/j.issn.1671-9352.0.2020.582

• • 上一篇    

Neumann边界条件分数阶扩散波方程的源项辨识

戚斌,程浩*   

  1. 江南大学理学院, 江苏 无锡 214122
  • 发布日期:2021-06-03
  • 作者简介:戚斌(1995— ),男,硕士研究生,研究方向为数学物理方程反问题. E-mail:mailbox957bin@163.com*通信作者简介:程浩(1983— ),男,博士,副教授,研究方向为数学物理方程反问题. E-mail:chenghao@jiangnan.edu.cn
  • 基金资助:
    江苏省研究生科研与实践创新计划资助项目(KYCX20_1922);国家自然科学基金资助项目(61772013);江苏省自然科学基金资助项目(BK20190578)

Identification of source term for fractional diffusion-wave equation with Neumann boundary conditions

QI Bin, CHENG Hao*   

  1. School of Science, Jiangnan University, Wuxi 214122, Jiangsu, China
  • Published:2021-06-03

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摘要： 对Neumann边界条件时间分数阶扩散波方程的源项辨识问题进行研究,构造一种改进的迭代正则化方法,得到源项辨识问题的正则化解,给出先验和后验参数选取规则下源项的正则化解和精确解之间的误差估计。数值算例验证了迭代正则化方法的有效性。

关键词: 分数阶扩散波方程, 源项辨识, 迭代正则化, 误差估计

Abstract: The source term identification of the time-fractional diffusion-wave equation with Neumann boundary conditions is studied. An improved iterative regularization method is constructed to calculate the regularization solution of the source term. The error estimates between the regularization solution and the exact solution are given under the prior and the posterior regularization parameter choice rules. Numerical examples verify the effectiveness of the iterative regularization method.

Key words: fractional diffusion-wave equation, source term identification, iterative regularization, error estimate

中图分类号: 

  • O241.82
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