兰州大学机构库 >数学与统计学院
时间分数阶扩散波方程中阶数和空间源项的同时辨识
Alternative TitleSimultaneous identification of the order and spatial source term in a time-fractional diffusion wave equation
岳茜
Subtype硕士
Thesis Advisor魏婷
2023-05-20
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name理学硕士
Degree Discipline计算数学
Keyword时间分数阶扩散波方程 Time fractional diffusion wave equation 阶数和空间源项 order and space-dependent source term 唯一性 uniqueness 最速下降法 steepest descent method
Abstract

在本文中, 我们研究了由部分区域上观测数据确定时间分数阶扩散波方程的阶数和空间源项问题. 我们证明了所考虑的反问题的唯一性, 以及正演算子的 Lipschitz 连续性. 我们利用 Tikhonov 正则化方法将反问题转化为变分问题, 并且证明了在正则化参数的先验选取下, Tikhonov 型泛函的极小元存在并收敛于精确解. 最后我们采用加速的最速下降法求解变分问题, 通过三个一维数值实例验证了该方法的有效性.

Other Abstract

In this paper, we investigate the simultaneous identification problem of the order and space-dependent source term in a time fractional diffusion wave equation by using the data in a subdomain. We prove the uniqueness of the inverse problem and the Lipschitz continuity of the forward operator. We use the Tikhonov regularization method to transform the inverse problem into a variational problem, and prove that the minimizer of the Tikhonov type functional exists and converges to the exact solution under an a priori choice of the regularization parameter. Finally, we propose an accelerated steepest descent method to solve the variational problem, and verify the effectiveness of this method through three one-dimensional numerical examples.

Subject Area数学物理方程反问题
MOST Discipline Catalogue理学 - 数学
URL查看原文
Language中文
Other Code262010_220200931820
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/538397
Collection数学与统计学院
Affiliation
兰州大学数学与统计学院
Recommended Citation
GB/T 7714
岳茜. 时间分数阶扩散波方程中阶数和空间源项的同时辨识[D]. 兰州. 兰州大学,2023.
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