兰州大学机构库 >数学与统计学院
分数阶扩散波方程的阶数和时间源项同时辨识问题
Alternative TitleSimultaneous identification of the order and time source term for a fractional diffusion wave equation
韦战
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应用数学
Keyword时间分数阶扩散波方程 Time fractional diffusion wave equation 分数阶阶数和时间源项 Fractional order and time source term, 唯一性 Uniqueness 交替极小化算法 Alternate minimization algorithm
Abstract

       本文主要考虑时间分数阶扩散波方程利用边界一点测量数据同时辨识分数阶阶数和时间源项问题。首先,基于正问题解的级数表达式,我们证明了正问题解的正则性和反问题解的唯一性。其次,我们把反问题转化为带有L2和TV正则项的正则化问题,并且采取交替极小化算法去求解正则化的变分问题。最后我们给出一些数值算例来验证算法的有效性。

Other Abstract

   In this paper, we consider the problem of simultaneous identification of the fractional order and time source term using a boundary point measurement data in a time fractional diffusion wave equation. Firstly, based on the series expression of the solution of the direct problem, we give the regularity of the solution of the direct problem and prove the uniqueness of the solution of the inverse problem considered in this thesis. Secondly, we transform the inverse problem into a regularization problem with L2 and TV regularization terms, and we adopt an alternate minimization algorithm to solve the regularized variational problem. Finally, some numerical examples are given to verify the effectiveness of the algorithm.

Subject Area数学物理方程反问题
MOST Discipline Catalogue理学 - 数学 - 应用数学
URL查看原文
Language中文
Other Code262010_220200931711
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/534938
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
韦战. 分数阶扩散波方程的阶数和时间源项同时辨识问题[D]. 兰州. 兰州大学,2023.
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