Stepwise regularization method for a nonlinear Riesz-Feller space-fractional backward diffusion problem

被引：4

作者：

Dang Duc Trong ^{[2
]}

Dinh Nguyen Duy Hai ^{[1
]}

Nguyen Dang Minh ^{[2
,3
]}

机构：

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

[2] Vietnam Natl Univ Ho Chi Minh City, Univ Sci, Dept Math & Comp Sci, Ho Chi Minh City, Vietnam

[3] Ho Chi Minh City Open Univ, Dept Fundamental Studies, Ho Chi Minh City, Vietnam

来源：

JOURNAL OF INVERSE AND ILL-POSED PROBLEMS | 2019年 / 27卷 / 06期

关键词：

Space-fractional backward diffusion problem; ill-posed problem; regularization; convergence estimate; INVERSE PROBLEM; CALCULUS; FOURIER;

D O I：

10.1515/jiip-2018-0033

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the backward diffusion problem for a space-fractional diffusion equation (SFDE) with a nonlinear source, that is, to determine the initial data from a noisy final data. Very recently, some papers propose new modified regularization solutions to solve this problem. To get a convergence estimate, they required some strongly smooth conditions on the exact solution. In this paper, we shall release the strongly smooth conditions and introduce a stepwise regularization method to solve the backward diffusion problem. A numerical example is presented to illustrate our theoretical result.

引用

页码：759 / 775

页数：17

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