Dang Duc Trong , Dinh Nguyen Duy Hai , Nguyen Dang Minh , Nguyen Nhu Lan
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引用次数: 0
Abstract
This paper deals with a fractional sideways problem of determining the surface temperature of a heat body from two interior temperature measurements. Mathematically, it is formulated as a problem for the one-dimensional heat equation with Caputo fractional time derivative of order , where the data are given at two interior points, namely and , and the solution is determined for . The problem is challenging since it is severely ill-posed for . For the ill-posed problem, we apply the Tikhonov regularization method in Hilbert scales to construct stable approximation problems. Using the two-parameter Tikhonov regularization, we obtain the order optimal convergence estimates in Hilbert scales by using both a priori and a posteriori parameter choice strategies. Numerical experiments are presented to show the validity of the proposed method.
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