兰州大学机构库 >数学与统计学院
基于分裂Bregman迭代方法的时间分数阶扩散波方程 空间源项辨识问题
Alternative Title)The split Bregman iteration method for determining the space-dependent source function in a time-fractional diffusion-wave equation
刘异
Subtype硕士
Thesis Advisor魏婷
2020-05-17
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name理学硕士
Degree Discipline应用数学
Keyword反空间源项 时间分数阶扩散波方程 分裂Bregman迭代方法
Abstract本文主要研究时间分数阶扩散波方程非光滑空间源项的辨识问题。首先由正问题解 的级数表达式,将反问题转化为求解第一类Fredholm积分方程,讨论反问题的解的存在 唯一性及不适定性。在本文中,考虑一种L2(Ω)与TV 混合罚项的Banach空间的正则化方 法,将反问题转化为正则化变分问题,给出正则化解的存在唯一性,稳定性,收敛性,收 敛阶分析。然后通过分裂Bregman迭代方法来快速获得近似解。最后,我们分别给出几个 一维和二维的数值算例来展示算法的有效性
Other AbstractThis paper mainly considers the inverse non-smooth space-dependent source problem for a time-fractional diffusion-wave equation. Firstly, based on the series expression of the solution for the direct problem, we transform the inverse problem into solving a Fredholm integral equation of the first kind, then we discuss the uniqueness and ill-posedness of the inverse problem. In this paper, we use a Banach regularization method of mixed penalty terms with L2(Ω) and TV for converting the inverse problem into a regularized variational problem and give the existence and uniqueness of regularization solution, convergence, and analysis of convergence order. Then we obtain an approximate solution quickly by using the split Bregman iteration method. In the end, numerical results for several examples in one-dimensional and two-dimensional cases show that the algorithm is efficient.
Pages40
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/464185
Collection数学与统计学院
Affiliation
数学与统计学院
First Author AffilicationSchool of Mathematics and Statistics
Recommended Citation
GB/T 7714
刘异. 基于分裂Bregman迭代方法的时间分数阶扩散波方程 空间源项辨识问题[D]. 兰州. 兰州大学,2020.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Altmetrics Score
Google Scholar
Similar articles in Google Scholar
[刘异]'s Articles
Baidu academic
Similar articles in Baidu academic
[刘异]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[刘异]'s Articles
Terms of Use
No data!
Social Bookmark/Share
No comment.
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.