Identification of Source Term for the Time-Fractional Diffusion-Wave Equation by Fractional Tikhonov Method

被引：6

作者：

Le Dinh Long ^{[1
]}

Nguyen Hoang Luc ^{[2
]}

Zhou, Yong ^{[3
,4
]}

Can Nguyen ^{[5
]}

机构：

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

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

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

[4] King Abdulaziz Univ, Fac Sci, Nonlinear Anal & Appl Math NAAM Res Grp, Jeddah 21589, Saudi Arabia

[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 / 10期

关键词：

fractional diffusion-wave equation; fractional derivative; ill-posed problem; Tikhonov regularization method; INVERSE SOURCE PROBLEM;

D O I：

10.3390/math7100934

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we consider an inverse problem to determine an unknown source term in a space-time-fractional diffusion equation. The inverse problems are often ill-posed. By an example, we show that this problem is NOT well-posed in the Hadamard sense, i.e., this problem does not satisfy the last condition-the solution's behavior changes continuously with the input data. It leads to having a regularization model for this problem. We use the Tikhonov method to solve the problem. In the theoretical results, we also propose a priori and a posteriori parameter choice rules and analyze them.

引用

页数：24

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