Electron. J. Differential Equations, Vol. 2017 (2017), No. 122, pp. 1-16.

Fourier truncation method for an inverse source problem for space-time fractional diffusion equation

Nguyen Huy Tuan, Le Dinh Long

In this article, we study an inverse problem to determine an unknown source term in a space time fractional diffusion equation, whereby the data are obtained at a certain time. In general, this problem is ill-posed in the sense of Hadamard, so the Fourier truncation method is proposed to solve the problem. In the theoretical results, we propose a priori and a posteriori parameter choice rules and analyze them.

Submitted March 5, 2017. Published May 4, 2017.
Math Subject Classifications: 35B53, 35R11.
Key Words: Fractional diffusion equation; Cauchy problem; Ill-posed problem; convergence estimates.

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Nguyen Huy Tuan
Applied Analysis Research Group
Faculty of Mathematics and Statistics
Ton Duc Thang University
Ho Chi Minh City, Viet Nam
email: nguyenhuytuan@tdt.edu.vn
Le Dinh Long
Institute of Computational Science and Technology
Ho Chi Minh City, Viet Nam
email: long04011990@gmail.com

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