An Iterative Regularization Method for Solving Backward Problems With 2 Perturbation Data

Q4 Mathematics
YUAN Xiaoyu, FENG Xiaoli, ZHANG Yun
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引用次数: 0

Abstract

The backward problem of space-fractional diffusion equations with perturbed diffusion coefficients and perturbed final data was considered. The initial data were recovered from the measured data at the final time. Given the severe ill-posedness of this problem, an iterative regularization method was proposed to tackle it. The convergence error estimate between the exact and approximate solutions was obtained under the assumption of an a-priori bound on the exact solution. Finally, several numerical simulations were conducted to verify the effectiveness of this method.
一种求解双扰动数据倒推问题的迭代正则化方法
研究了具有摄动扩散系数和摄动最终数据的空间分数扩散方程的后向问题。从最后一次的测量数据中恢复初始数据。针对该问题的严重病态性,提出了一种迭代正则化方法来解决该问题。在精确解有先验界的假设下,得到了精确解和近似解之间的收敛误差估计。最后,通过数值仿真验证了该方法的有效性。
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来源期刊
应用数学和力学
应用数学和力学 Mathematics-Applied Mathematics
CiteScore
1.20
自引率
0.00%
发文量
6042
期刊介绍: Applied Mathematics and Mechanics was founded in 1980 by CHIEN Wei-zang, a celebrated Chinese scientist in mechanics and mathematics. The current editor in chief is Professor LU Tianjian from Nanjing University of Aeronautics and Astronautics. The Journal was a quarterly in the beginning, a bimonthly the next year, and then a monthly ever since 1985. It carries original research papers on mechanics, mathematical methods in mechanics and interdisciplinary mechanics based on artificial intelligence mathematics. It also strengthens attention to mechanical issues in interdisciplinary fields such as mechanics and information networks, system control, life sciences, ecological sciences, new energy, and new materials, making due contributions to promoting the development of new productive forces.
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