Abstract
This paper is devoted to identifying an unknown source for a time-fractional diffusion equation with variable coefficients in a general bounded domain. This is an ill-posed problem. Firstly, we obtain a regularization solution by the Landweber iterative regularization method. The convergence estimates between regularization solution and exact solution are given under a priori and a posteriori regularization parameter choice rules, respectively. The convergence estimates we obtain are optimal order for any p in two parameter choice rules, i.e., it does not appear to be a saturating phenomenon. Finally, the numerical examples in the one-dimensional and two-dimensional cases show our method is feasible and effective.
Highlights
Nowadays, the study of time-fractional diffusion equations has drawn attention from various disciplines of science and engineering, such as mechanical engineering [, ], viscoelasticity [ ], Lévy motion [ ], electron transport [ ], dissipation [ ], heat conduction [ – ] and high-frequency financial data [ ]
In [ ], Wang solved a backward problem for a time-fractional diffusion equation with variable coefficients in a general bounded domain by the Tikhonov regularization method
6 Conclusion In this paper, we consider an inverse problem for identifying an unknown source for a time-fractional diffusion equation with variable coefficients defined in a general domain
Summary
The study of time-fractional diffusion equations has drawn attention from various disciplines of science and engineering, such as mechanical engineering [ , ], viscoelasticity [ ], Lévy motion [ ], electron transport [ ], dissipation [ ], heat conduction [ – ] and high-frequency financial data [ ]. In [ ], the authors considered the backward inverse problem for a time-fractional diffusion equation. In [ ], Liu and Yamamoto used the quasi-reversibility method to solve a backward problem for a time-fractional diffusion equation in the onedimensional case. In [ ], Wang solved a backward problem for a time-fractional diffusion equation with variable coefficients in a general bounded domain by the Tikhonov regularization method.
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