| 时间分数阶扩散方程反初值问题 |
| Alternative Title | An inverse initial value problem for a time-fractional difussion equation
|
| 刘建丽 |
| Thesis Advisor | 魏婷
|
| 2016-05-21
|
| Degree Grantor | 兰州大学
|
| Place of Conferral | 兰州
|
| Degree Name | 硕士
|
| Keyword | 反初值问题
分数阶扩散方程
极小化泛函
收敛阶
|
| Abstract | 本文我们考虑了时间分数阶扩散方程反初值问题, 即由带误差的终端数据来反演初始数据. 由于反问题的不适定性, 我们提出一个正则化方法, 即构造一个Hilbert尺度空间下的极小化泛函, 并将它的极小元作为正则化解来求解这个反问题. 进一步我们得到了先验正则化参数的选取和后验正则化参数的选取两种情况下的误差估计和收敛阶. 最后我们给出一维和二维情况下的数值算例来说明我们所提出的方法是有效和稳定的. |
| Other Abstract | In this thesis,we consider an inverse initial value problem for a time-fractional diffusion equation.That is to determine the initial data from a noisy final data. Since the inverse problem is ill-posed,then we propose a regularization method.Construct a minimization functional in Hilbert scale space and take its minimization solution as the regularization solution to deal with the inverse problem.Furthermore we obtain two kinds of convergence rates by using an priori regularization parameter choice rule and an a posteriori regularization parameter choice rule. Numerical examples in one-dimensional and two-dimensional cases are provided to show the effectiveness and stability of the proposed methods. |
| URL | 查看原文
|
| Language | 中文
|
| Document Type | 学位论文
|
| Identifier | https://ir.lzu.edu.cn/handle/262010/224714
|
| Collection | 数学与统计学院
|
Recommended Citation
GB/T 7714 |
刘建丽. 时间分数阶扩散方程反初值问题[D]. 兰州. 兰州大学,2016.
|
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
