| 求解分数阶方程源项辨识问题的一种拟边值正则化方法 | |
| Alternative Title | A quasi-boundary value regularization method for solving the source term identification problem of the fractional equation |
| 罗玉花 | |
| 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 | 应用数学 |
| Keyword | 时间分数阶扩散波方程 空间源项辨识问题 推广的拟边值正则化方法 收敛阶 |
| Abstract | 这篇文章主要研究了在有界区域上时间分数阶扩散波方程空间依赖源项的辨识问题。首先，通过正问题解的级数表达式将原问题转化为第一类的Fredholm积分方程，然后我们考虑了空间源项辨识问题的唯一性，不适定性和条件稳定性。进一步，我们提出一种推广的拟边值正则化方法来求解此空间源项辨识问题，同时证明了正则化问题的适定性，并且给出了在一个先验正则化参数选取和一个后验正则化参数选取下正则化解的收敛阶。最后由一些一维和二维情形下的数值例子来证实我们的理论结果。 |
| Other Abstract | This paper is devoted to identifying a space-dependent source term for a time fractional diffusion-wave equationin a bounded domain. By the series expression of the solution for the direct problem, the original problem can be transformed intoa first kind of Fredholm integral equation.The uniqueness, ill-posedness and conditional stability of this space-dependent source term identification problem are considered. Then we propose a generalized quasi-boundary value regularization method to solve the space-dependent source term identification problem and also prove that the regularization problem is well-posed. Further, two kindsof convergence rates for the regularized solution can be proved by using an a priori and an a posteriori regularization parameter choice rule, respectively. Numerical examples in one-dimensional case and two-dimensional caseare given to confirm our theoretical results. |
| Pages | 46 |
| URL | 查看原文 |
| Language | 中文 |
| Document Type | 学位论文 |
| Identifier | https://ir.lzu.edu.cn/handle/262010/460793 |
| 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 | 罗玉花. 求解分数阶方程源项辨识问题的一种拟边值正则化方法[D]. 兰州. 兰州大学,2021. |
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