Identification of the Initial Value for a Time-Fractional Diffusion Equation

被引：1

作者：

Yang, Fan ^{[1
]}

Gao, Yin-Xia ^{[1
]}

Li, Dun-Gang ^{[1
]}

Li, Xiao-Xiao ^{[1
]}

机构：

[1] Lanzhou Univ Technol, Sch Sci, Lanzhou 730050, Peoples R China

来源：

SYMMETRY-BASEL | 2022年 / 14卷 / 12期

基金：

中国国家自然科学基金;

关键词：

time-fractional diffusion equation; columnar symmetric domain; ill-posed problem; Landweber iterative method; TIKHONOV REGULARIZATION METHOD; INVERSE SOURCE PROBLEM; BACKWARD PROBLEM; WAVE EQUATION;

D O I：

10.3390/sym14122569

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In this manuscript, we study the inverse problem for identifying the initial value of a time-fractional diffusion equation in an axisymmetric region. This is an ill-posed problem, i.e., the solution does not depend continuously on the data. We choose the Landweber iterative regularization method to solve this problem. Under the a priori and the a posteriori regularization parameter choice rules, we present the error estimates between the regularization solutions and the exact solution. We present some examples to show this method's effectiveness.

引用

页数：11

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