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Identification of an inverse source problem for time‐fractional diffusion equation with random noise
Author(s) -
Thach Tran Ngoc,
Huy Tuan Nguyen,
Tam Pham Thi Minh,
Minh Mach Nguyet,
Can Nguyen Huu
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5334
Subject(s) - mathematics , inverse problem , regularization (linguistics) , diffusion equation , noise (video) , convergence (economics) , inverse , exact solutions in general relativity , filter (signal processing) , mathematical optimization , mathematical analysis , computer science , geometry , economy , artificial intelligence , economic growth , economics , image (mathematics) , service (business) , computer vision
In this paper, we consider an inverse source problem for a time fractional diffusion equation. In general, this problem is ill posed, therefore we shall construct a regularized solution using the filter regularization method in the random noise case. We will provide appropriate conditions to guarantee the convergence of the approximate solution to the exact solution. Then, we provide examples of filters in order to obtain error estimates for their approximate solutions. Finally, we present a numerical example to show efficiency of the method.