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Inverse source problem for a distributed-order time fractional diffusion equation

Content Provider	Scilit
Author	Cheng, Xiaoliang Yuan, Lele Liang, Kewei
Copyright Year	2019
Abstract	This paper studies an inverse source problem for a time fractional diffusion equation with the distributed order Caputo derivative. The space-dependent source term is recovered from a noisy final data. The uniqueness, ill-posedness and a conditional stability for this inverse source problem are obtained. The inverse problem is formulated into a minimization functional with Tikhonov regularization method. Further, based on the series representation of the regularized solution, we give convergence rates of the regularized solution under an a-priori and an a-posteriori regularization parameter choice rule. With an adjoint technique for computing the gradient of the regularization functional, the conjugate gradient method is applied to reconstruct the space-dependent source term. Two numerical examples illustrate the effectiveness of the proposed method.
Related Links	https://www.degruyter.com/downloadpdf/journals/jiip/28/1/article-p17.pdf http://www.degruyter.com/downloadpdf/j/jiip.ahead-of-print/jiip-2019-0006/jiip-2019-0006.xml
Ending Page	32
Page Count	16
Starting Page	17
ISSN	09280219
e-ISSN	15693945
DOI	10.1515/jiip-2019-0006
Journal	Journal of Inverse and Ill-Posed Problems
Issue Number	1
Volume Number	28
Language	English
Publisher	Walter de Gruyter GmbH
Publisher Date	2019-06-13
Access Restriction	Open
Subject Keyword	Journal of Inverse and Ill-posed Problems Applied Mathematics Inverse Source Problem Distributed-order Time Fractional Diffusion Equation Tikhonov Regularization Convergence Analysis A-priori Parameter Choice Morozov's Discrepancy Principle Journal: Journal of Inverse and Ill-Posed Problems, Vol- 28
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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