时空分数阶扩散波动方程的初值识别问题

摘要/Abstract

摘要：

研究具有时空分数阶导数的扩散波动方程的初值识别反问题. 分析该反问题的不适定性, 给出条件稳定性结果. 利用 Tikhonov 正则化方法恢复解的稳定性, 并分别给出在先验和后验正则化参数选取规则下, 正则解和精确解之间的误差估计. 通过数值算例说明 Tikhonov 正则化方法求解此类反问题非常有效.

关键词: 时空分数阶扩散波动方程, 不适定问题, 初值识别, Tikhonov 正则化方法, 误差估计

Abstract:

In this paper, we study the identification of unknown initial values of time-space fractional diffusion-wave matrix. Firstly, we prove that the problem is ill-posed and give the conditional stability result. Then, we use Tikhonov regularization method to restore the stability of the solutions, and give the convergence error estimates under a priori regularization parameter selection rule and a posteriori regularization parameter selection rule. Finally, numerical examples show that the regularization method is effective.

Key words: Time-space fractional diffusion-wave matrix, Ill-posed problem, Identify unknown initial values, Tikhonov regularization method, Error estimation

中图分类号:

O175

杨帆, 曹英, 李晓晓. 时空分数阶扩散波动方程的初值识别问题[J]. 数学物理学报, 2023, 43(2): 377-398.

Yang Fan, Cao Ying, Li Xiaoxiao. Identification of Initial Values of Space-Time Fractional Diffusion-Wave Equation[J]. Acta mathematica scientia,Series A, 2023, 43(2): 377-398.

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