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 in:	Mathematical modelling and analysis Vol. 29; no. 2; pp. 193 - 214
Main Authors:	Yang, Fan, Xu, Jian-ming, Li, Xiao-xiao
Format:	Journal Article
Language:	English
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
Online Access:	Get full text
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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.
ISSN:	1392-6292 1648-3510
DOI:	10.3846/mma.2024.18133