Work

Two Regularization Methods for Identifying the Unknown Source of Sobolev Equation With Fractional Laplacian

Year: 2025

Type: article

Abstract: In this paper, an inverse source problem for the Sobolev equation with fractional Laplacian is investigated. We prove that this kind of problem is ill-posed and apply the Quasi-boundary regularization method and fractional Landweber iterative regularization method to solve this inverse problem. Based on the result of conditional stability, the error estimates between the exact solution and the regularization solution are given under the priori and posteriori regularization parameter selection rules. Finally, three examples are given to illustrate the effectiveness and feasibility of these methods.

Source: Journal of Applied Analysis & Computation

DOI: 10.11948/20240065

Authors: Fan Yang, Lu-Lu Yan, Hao Liu, Xiao-Xiao Li

Institution: Lanzhou University of Technology

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Natural Science Foundation of China

Award: 两类分数阶扩散-波动方程若干反问题的正则化方法和算法研究