Determination of Initial Distribution for a Space-Fractional Diffusion Equation with Time-Dependent Diffusivity

被引：0
作者：
Tran Nhat Luan
Tra Quoc Khanh
机构：
[1] Institute for Computational Science and Technology,Division of Computational Mathematics and Engineering, Institute for Computational Science
[2] Ton Duc Thang University,Faculty of Mathematics and Statistics
[3] Ton Duc Thang University,undefined
来源：
Bulletin of the Malaysian Mathematical Sciences Society | 2021年 / 44卷
关键词：
Space-fractional diffusion equation; Ill-posed problem; Filter regularization; Lipschitz continuity; 65N20; 35R25; 47J06; 26A33;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In the present paper, we devote our aspiration to some initial and final value problems for a class of space-fractional diffusion equation with time-dependent diffusivity factor. For the initial value problem (IVP), we investigate the stability of the solution concerning the data and the fractional order. For the final value problem, we prove the ill-posedness and suggest a filter method to regularize the problem. Explicit convergence rate of Hölder type is established. Finally, several numerical examples based on the finite difference approximation and the discrete Fourier transform are performed to demonstrate the effectiveness of the proposed method.
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页码：3461 / 3487
页数：26
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