分数阶椭圆方程反边值问题的分数 Tikhonov 正则化方法

Abstract

Abstract:

In this paper, we study an inverse boundary value problem for fractional elliptic equation of Tricomi-Gellerstedt-Keldysh-type. For this ill-posed problem, a conditional stability result is established. Based on the ill-posedness analysis, a fractional Tikhonov regularization method was constructed to recover the continuous dependence of the solution on the measurement data. Under the a-priori and a-posteriori selection rules for regularization parameter, the corresponding convergence results of Hölder type are derived and proved, respectively. Finally, the simulation effectiveness of the fractional Tikhonov method is verified by two numerical examples. The numerical results show that the method works stably and effectively in dealing with the inverse problem in the text.

Key words: Inverse boundary value problem, Fractional elliptic equation, Fractional Tikhonov regularization, A-priori and a-posteriori convergence estimates, Numerical simulation

CLC Number:

O175

Zhang Xiao, Zhang Hongwu. Fractional Tikhonov Regularization Method for an Inverse Boundary Value Problem of the Fractional Elliptic Equation[J].Acta mathematica scientia,Series A, 2024, 44(4): 978-993.

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Fractional Tikhonov Regularization Method for an Inverse Boundary Value Problem of the Fractional Elliptic Equation

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