A Mollification Regularization Method for the Inverse Source Problem for a Time Fractional Diffusion Equation

被引：8

作者：

Le Dinh Long ^{[1
]}

Yong Zhou ^{[2
,3
]}

Tran Thanh Binh ^{[4
]}

Nguyen Can ^{[5
]}

机构：

[1] Thu Dau Mot Univ, Fac Nat Sci, Thu Dau Mot City 820000, Binh Duong Prov, Vietnam

[2] Macau Univ Sci & Technol, Fac Informat Technol, Macau 999078, Peoples R China

[3] Xiangtan Univ, Fac Math & Computat Sci, Xiangtan 411105, Peoples R China

[4] Duy Tan Univ, Inst Res & Dev, Da Nang 550000, Vietnam

[5] Ton Duc Thang Univ, Fac Math & Stat, Appl Anal Res Grp, Ho Chi Minh City 700000, Vietnam

来源：

MATHEMATICS | 2019年 / 7卷 / 11期

关键词：

time-fractional diffusion equation; inverse problem; ill-posed problem; convergence estimates;

D O I：

10.3390/math7111048

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a time-fractional diffusion equation for an inverse problem to determine an unknown source term, whereby the input data is obtained at a certain time. In general, the inverse problems are ill-posed in the sense of Hadamard. Therefore, in this study, we propose a mollification regularization method to solve this problem. In the theoretical results, the error estimate between the exact and regularized solutions is given by a priori and a posteriori parameter choice rules. Besides, the proposed regularized methods have been verified by a numerical experiment.

引用

页数：19

共 21 条

[1]

[Anonymous], 2006, MITTAG LEFFLER FUNCT

[2] From continuous time random walks to the fractional Fokker-Planck equation [J].

Barkai, E ;

Metzler, R ;

Klafter, J .

PHYSICAL REVIEW E, 2000, 61 (01) :132-138

[3] Finite element multigrid method for multi-term time fractional advection diffusion equations [J].

Bu, Weiping ;

Liu, Xiangtao ;

Tang, Yifa ;

Yang, Jiye .

INTERNATIONAL JOURNAL OF MODELING SIMULATION AND SCIENTIFIC COMPUTING, 2015, 6 (01)

[4] A fractional diffusion equation to describe Levy flights [J].

Chaves, AS .

PHYSICS LETTERS A, 1998, 239 (1-2) :13-16

[5] Application of the variational iteration method to inverse heat source problems [J].

Geng, Fazhan ;

Lin, Yingzhen .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2009, 58 (11-12) :2098-2102

[6]

Gorenflo R., 2001, MATH FINANC, P171, DOI 10.1007/978-3-0348-8291-017

[7] Regularized solution of an inverse source problem for a time fractional diffusion equation [J].

Huy Tuan Nguyen ;

Dinh Long Le ;

Van Thinh Nguyen .

APPLIED MATHEMATICAL MODELLING, 2016, 40 (19-20) :8244-8264

[8]

Kirsch A., 2011, INTRO MATH THEORY IN

[9] AN INVERSE SOURCE PROBLEM FOR HEAT-EQUATION [J].

MALYSHEV, I .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1989, 142 (01) :206-218

[10]

Mathai A.M., 2008, SPECIAL FUNCTIONS AP

← 1 2 3 →