Abstract
We investigate the linear but ill-posed inverse problem of determining a multi-dimensional space-dependent heat source in a time-fractional diffusion equation. We show that the problem is ill-posed in the Hilbert scale Hr(Rn) and establish global order optimal lower bound for the worst case error. Next, we use the Tikhonov regularization method to deal with this problem in the Hilbert scale Hr(Rn). Locally optimal choices of parameters for the family of regularization operator in the Hilbert scales Hr(Rn) are analyzed by a-priori and a-posteriori methods. Numerical implementations are presented to illustrate our theoretical findings.
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