RECOVERING A SPACE-DEPENDENT SOURCE TERM IN A TIME-FRACTIONAL DIFFUSION WAVE EQUATION | Zendy

Ting Wei | Zendy; Xiongbin Yan | Zendy

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RECOVERING A SPACE-DEPENDENT SOURCE TERM IN A TIME-FRACTIONAL DIFFUSION WAVE EQUATION

Author(s) -

Ting Wei,

Xiongbin Yan

Publication year - 2019

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/20180318

Subject(s) - tikhonov regularization , uniqueness , mathematics , inverse problem , regularization (linguistics) , mathematical analysis , conjugate gradient method , wave equation , diffusion equation , term (time) , mathematical optimization , computer science , physics , economy , quantum mechanics , artificial intelligence , economics , service (business)

This work is concerned with identifying a space-dependent source function from noisy final time measured data in a time-fractional diffusion wave equation by a variational regularization approach. We provide a regularity of direct problem as well as the existence and uniqueness of adjoint problem. The uniqueness of the inverse source problem is discussed. Using the Tikhonov regularization method, the inverse source problem is formulated into a variational problem and a conjugate gradient algorithm is proposed to solve it. The efficiency and robust of the proposed method are supported by some numerical experiments.

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