兰州大学机构库 >数学与统计学院
分数阶偏微分方程几类反问题的正则化方法
Alternative TitleRegularization methods for some inverse problems of fractional PDEs
郑光辉
Thesis Advisor魏婷
2012-05-30
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name博士
Keyword分数阶偏微分方程 反问题 边界识别问题 时间分数阶逆对流扩散问题 时间分数阶对流扩散Cauchy 问题 时间分数阶扩散Cauchy 问题
Abstract在本文中, 我们主要考虑了分数阶偏微分方程中的几类反问题, 例如时间分数阶逆对流扩散问题(TFIADP), 时间分数阶对流扩散Cauchy 问题(TFADCP), 时间分数阶扩散Cauchy 问题(TFDCP), 时间分数阶逆扩散问题(TFIDP) 以及空间分数阶逆时扩散问题(SFBDP). 随后, 还考虑了多层区域上抛物型系统在线性和非线性接触条件下的边界识别问题(BIP), 以及一般抛物方程中同时反演源项和初值的问题.
Other AbstractIn this thesis, we consider several inverse problems in fractional PDEs, such as time fractional inverse advection-dispersion problem (TFIADP), time fractional advection-dispersion Cauchy problem (TFADCP), time fractional diffusion Cauchy problem (TFDCP), time fractional inverse diffusion problem (TFIDP) and space fractional backward diffusion problem (SFBDP). Moreover, we consider boundary identification problems (BIP) in the parabolic system with a multi-layer domain, which refer to linear and nonlinear interface conditions, and recovering the source and initial value simultaneously in a parabolic equation. Fractional PDEs have been used recently to describe a range of problems in physical, chemical, biology, finance, signal processing, systems identification, control theory and so on. As for direct problems in fractional PDEs, there are a lot of researches both in fundamental theory and numerical computation. However, the result for the corresponding inverse problems is still very sparse. In this thesis, we propose a new convolution-type regularization method to solve time fractional inverse advection-dispersion problem (TFIADP), time fractional diffusion Cauchy problem (TFDCP), time fractional inverse diffusion problem (TFIDP), space fractional backward diffusion problem (SFBDP), and convergence estimates of the regularization method are presented. Furthermore, we apply spectral regularization method to solve the time fractional inverse advection-dispersion problem (TFIADP), time fractional advection-dispersion Cauchy problem (TFADCP), space fractional backward diffusion problem (SFBDP) and obtain the corresponding convergence estimates. Finally, we make numerical tests for above two regularization methods to show the effectiveness. The boundary identification problem (BIP) is very important in the research area of inverse problems in PDEs, and has wide application background. Because of ill-posedness and nonlinearity, the boundary identification problems are very challenging. Here, we obtain the stability estimates and uniqueness for the boundary identification problems in the parabolic system with a multi-layer domain. Under some given measurement data, it is a hot topic to recover simultaneously two goals, even more goals in inverse problems. Because it need to recover more goals, it is harder than conventional inverse problems. We investigate recovering the source and initial value simultaneously in a parabolic equation. Stability esti...
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/225421
Collection数学与统计学院
Recommended Citation
GB/T 7714
郑光辉. 分数阶偏微分方程几类反问题的正则化方法[D]. 兰州. 兰州大学,2012.
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
[郑光辉]'s Articles
Baidu academic
Similar articles in Baidu academic
[郑光辉]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[郑光辉]'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.