时间分数阶扩散方程的Cauchy问题

兰州大学机构库 >数学与统计学院

	时间分数阶扩散方程的Cauchy问题
Alternative Title	The Cauchy problem for a time-fractional diffusion equation
	李红波
Thesis Advisor	魏婷
	2015-05-29
Degree Grantor	兰州大学
Place of Conferral	兰州
Degree Name	硕士
Keyword	Cauchy 问题 Cauchy 数据变分问题共轭梯度法
Abstract	本文中，我们考虑时间分数阶扩散方程的Cauchy问题，即由一部分边界上的Cauchy数据决定另一部分边界上的Cauchy数据。我们首先把此反问题转化成一个变分问题，构造出一个正则化泛函，然后借助灵敏度问题和伴随问题求此泛函的梯度，最后用共轭梯度法求解这个变分问题。在反问题的求解过程中，会涉及到相应正问题的计算方法，我们使用有限差分方法解决每一步迭代的正问题。数值举例表明这种方法是有效并且稳定的。
Other Abstract	In this paper, we consider a Cauchy problem of the time fractional diffusion equation for determining the Cauchy data at one part of the boundary from the Cauchy data at the other part. The variational formulation of the problem is given. And we deduce the gradient of the regularization functional based on a sensitivity problem and an adjoint problem. Then the conjugate gradient method is proposed for solving the variational problem, in which the finite difference method is used to solve the direct problem. Several numerical examples are provided to show the effectiveness and robustness of the proposed method.
URL	查看原文
Language	中文
Document Type	学位论文
Identifier	https://ir.lzu.edu.cn/handle/262010/224718
Collection	数学与统计学院
Recommended Citation GB/T 7714	李红波. 时间分数阶扩散方程的Cauchy问题[D]. 兰州. 兰州大学,2015.

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