| 一种拟逆方法辨识时间分数阶扩散波方程的空间源项 | |
| Alternative Title | A quasi-reversibility method to identify a space-dependent source for a time-fractional diffusion-wave equation |
| 王亚娟 | |
| Subtype | 硕士 |
| Thesis Advisor | 魏婷 |
| 2021-05-22 | |
| Degree Grantor | 兰州大学 |
| Place of Conferral | 兰州 |
| Degree Name | 理学硕士 |
| Degree Discipline | 计算数学 |
| Keyword | 分数阶扩散波方程 源项辨识问题 拟逆正则化方法. |
| Abstract | 在本文中, 我们主要研究在有界区域上的时间分数阶扩散波方程的空间源项反演问题, 即通过带有误差的终端数据来反演空间源项. 首先, 基于正问题解的级数表达式, 将反问题转化为第一类积分方程, 讨论反问题解的唯一性, 不适定性及条件稳定性. 然后, 我们提出一种拟逆正则化方法将反问题转化成一个正则化问题, 并证明了该正则化问题的适定性, 分别考虑了先验选取和后验选取正则化参数下的收敛阶估计. 最后通过数值算例来说明理论的正确性及正则化方法的有效性. |
| Other Abstract | In this paper, we study a problem of recovering a space-dependent source term for a time-fractional diffusion-wave equation in a bounded domain, that is, we use the final time noisy data to recover the space-dependent source.Firstly,based on the series expression of the solution about the direct problem, the inverse problem is transformed into the first kind of integral equation, we discuss the uniqueness,ill-posedness and conditional stability of the inverse problem. Then we propose a quasi-reversibility regularization method to transform the inverse problem into a regularied problem, and prove the well-posedness of the regularied problem,and give two convergence order estimations by using an a priori and an a posteriori choice rule for the regularization parameter respectively. Finally, numerical examples are presented which demonstrate the effectiveness of the regularization methods and confirm the theoretical results. |
| Pages | 49 |
| URL | 查看原文 |
| Language | 中文 |
| Document Type | 学位论文 |
| Identifier | https://ir.lzu.edu.cn/handle/262010/460745 |
| Collection | 数学与统计学院 |
| Affiliation | 数学与统计学院 |
| First Author Affilication | School of Mathematics and Statistics |
| Recommended Citation GB/T 7714 | 王亚娟. 一种拟逆方法辨识时间分数阶扩散波方程的空间源项[D]. 兰州. 兰州大学,2021. |
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