The Fractional Tikhonov Regularization Method to Identify the Initial Value of the Nonhomogeneous Time-Fractional Diffusion Equation on a Columnar Symmetrical Domain

In this paper, the inverse problem for identifying the initial value of a time fractional nonhomogeneous diffusion equation in a columnar symmetric region is studied. This is an ill-posed problem, i.e., the solution does not depend continuously on the data. The fractional Tikhonov regularization met...

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Bibliographic Details
Published inSymmetry (Basel) Vol. 14; no. 8; p. 1633
Main Authors Chen, Yong-Gang, Yang, Fan, Li, Xiao-Xiao, Li, Dun-Gang
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.08.2022
Subjects
columnar symmetric domain
Diffusion
Exact solutions
fractional Tikhonov method
Identification methods
Ill posed problems
ill-posed problem
Inequality
Inverse problems
Regularization
Regularization methods
time-fractional nonhomogeneous diffusion equation
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Summary:In this paper, the inverse problem for identifying the initial value of a time fractional nonhomogeneous diffusion equation in a columnar symmetric region is studied. This is an ill-posed problem, i.e., the solution does not depend continuously on the data. The fractional Tikhonov regularization method is applied to solve this problem and obtain the regularization solution. The error estimations between the regularization solution and the exact solution are also obtained under the priori and the posteriori regularization parameter choice rules, respectively. Some examples are given to show this method’s effectiveness.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14081633