MODIFIED LANDWEBER ITERATIVE METHOD FOR A BACKWARD PROBLEM IN TIME OF THE DIFFUSION EQUATION WITH LOCAL AND NONLOCAL OPERATORS

doi:10.1007/s10473-025-0324-2

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (3): 1205-1222.doi: 10.1007/s10473-025-0324-2

MODIFIED LANDWEBER ITERATIVE METHOD FOR A BACKWARD PROBLEM IN TIME OF THE DIFFUSION EQUATION WITH LOCAL AND NONLOCAL OPERATORS

Hongwu ZHANG, Yanhui LI^†

School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China

收稿日期:2023-10-26 修回日期:2024-03-18 出版日期:2025-05-25 发布日期:2025-09-30

MODIFIED LANDWEBER ITERATIVE METHOD FOR A BACKWARD PROBLEM IN TIME OF THE DIFFUSION EQUATION WITH LOCAL AND NONLOCAL OPERATORS

Hongwu ZHANG, Yanhui LI^†

School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China

Received:2023-10-26 Revised:2024-03-18 Online:2025-05-25 Published:2025-09-30
Contact: ^†Yanhui LI, E-mail: liyan_h@163.com
About author:Hongwu ZHANG, E-mail: zh-hongwu@163.com
Supported by:
NSF of Ningxia (2022AAC03234), the NSF of China (11761004), the Construction Project of First-Class Disciplines in Ningxia Higher Education (NXYLXK2017B09), and the Postgraduate Innovation Project of North Minzu University (YCX23074).

摘要/Abstract

摘要： In this article, we consider a backward problem in time of the diffusion equation with local and nonlocal operators. This inverse problem is ill-posed because the solution does not depend continuously on the measured data. Inspired by the classical Landweber iterative method and Fourier truncation technique, we develops a modified Landweber iterative regularization method to restore the continuous dependence of solution on the measurement data. Under the a-priori and a-posteriori choice rules for the regularized parameter, the convergence estimates for the regularization method are derived. Some results of numerical simulation are provided to verify the stability and feasibility of our method in dealing with the considered problem.

关键词: backward problem in time, diffusion equation with local and nonlocal operators, modified Landweber regularization, convergence estimate, numerical simulation

Abstract: In this article, we consider a backward problem in time of the diffusion equation with local and nonlocal operators. This inverse problem is ill-posed because the solution does not depend continuously on the measured data. Inspired by the classical Landweber iterative method and Fourier truncation technique, we develops a modified Landweber iterative regularization method to restore the continuous dependence of solution on the measurement data. Under the a-priori and a-posteriori choice rules for the regularized parameter, the convergence estimates for the regularization method are derived. Some results of numerical simulation are provided to verify the stability and feasibility of our method in dealing with the considered problem.

Key words: backward problem in time, diffusion equation with local and nonlocal operators, modified Landweber regularization, convergence estimate, numerical simulation

中图分类号:

35R25

Hongwu ZHANG, Yanhui LI. MODIFIED LANDWEBER ITERATIVE METHOD FOR A BACKWARD PROBLEM IN TIME OF THE DIFFUSION EQUATION WITH LOCAL AND NONLOCAL OPERATORS[J]. 数学物理学报(英文版), 2025, 45(3): 1205-1222.

Hongwu ZHANG, Yanhui LI. MODIFIED LANDWEBER ITERATIVE METHOD FOR A BACKWARD PROBLEM IN TIME OF THE DIFFUSION EQUATION WITH LOCAL AND NONLOCAL OPERATORS[J]. Acta mathematica scientia,Series B, 2025, 45(3): 1205-1222.

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MODIFIED LANDWEBER ITERATIVE METHOD FOR A BACKWARD PROBLEM IN TIME OF THE DIFFUSION EQUATION WITH LOCAL AND NONLOCAL OPERATORS

MODIFIED LANDWEBER ITERATIVE METHOD FOR A BACKWARD PROBLEM IN TIME OF THE DIFFUSION EQUATION WITH LOCAL AND NONLOCAL OPERATORS

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