Simultaneous inversion of the source term and initial value of the time fractional diffusion equation

In this paper, the problem we investigate is to simultaneously identify the source term and initial value of the time fractional diffusion equation. This problem is ill-posed, i.e., the solution (if exists) does not depend on the measurable data. We give the conditional stability result under the a-...

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Bibliographic Details
Published inMathematical modelling and analysis Vol. 29; no. 2; pp. 193 - 214
Main Authors Yang, Fan, Xu, Jian-ming, Li, Xiao-xiao
Format Journal Article
LanguageEnglish
Published Vilnius Vilnius Gediminas Technical University 26.03.2024
Subjects
Boundary conditions
Dissolution
Engineering mathematics
Exact solutions
Functions, Inverse
Heat equation
Identification
ill-posed
inverse problem
Inverse problems
modified Tikhonov method
Regularization
Regularization methods
source term and initial value
Tests, problems and exercises
time fractional diffusion equation
China
inverse problem
time fractional diffusion equation
source term and initial value
modified Tikhonov method
ill-posed
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Summary:In this paper, the problem we investigate is to simultaneously identify the source term and initial value of the time fractional diffusion equation. This problem is ill-posed, i.e., the solution (if exists) does not depend on the measurable data. We give the conditional stability result under the a-priori bound assumption for the exact solution. The modified Tikhonov regularization method is used to solve this problem, and under the a-priori and the a-posteriori selection rule for the regularization parameter, the convergence error estimations for this method are obtained. Finally, numerical example is given to prove the effectiveness of this regularization method.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1392-6292
1648-3510
DOI:10.3846/mma.2024.18133