Regularization for a Sideways Problem of the Non-Homogeneous Fractional Diffusion Equation

被引：0

作者：

Chen, Yonggang ^{[1
]}

Qiao, Yu ^{[2
]}

Xiong, Xiangtuan ^{[2
]}

机构：

[1] China Univ Petr East China, Sch Sci, Qingdao 266580, Peoples R China

[2] Northwest Normal Univ, Dept Math, Lanzhou 730070, Peoples R China

来源：

FRACTAL AND FRACTIONAL | 2022年 / 6卷 / 06期

关键词：

sideways problem; non-homogeneous fractional diffusion equation; ill-posedness; stability estimate; regularization method; HEAT-CONDUCTION PROBLEM; NUMERICAL-SOLUTION; INVERSE PROBLEM; CAUCHY-PROBLEM; WAVELET; FLUX;

D O I：

10.3390/fractalfract6060312

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we investigate a sideways problem of the non-homogeneous time-fractional diffusion equation, which is highly ill-posed. Such a model is obtained from the classical non-homogeneous sideways heat equation by replacing the first-order time derivative by the Caputo fractional derivative. We achieve the result of conditional stability under an a priori assumption. Two regularization strategies, based on the truncation of high frequency components, are constructed for solving the inverse problem in the presence of noisy data, and the corresponding error estimates are proved.

引用

页数：22

共 46 条

[1] Modeling attractors of chaotic dynamical systems with fractal-fractional operators [J].

Atangana, Abdon ;

Qureshi, Sania .

CHAOS SOLITONS & FRACTALS, 2019, 123 :320-337

[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] DETERMINING SURFACE TEMPERATURES FROM INTERIOR OBSERVATIONS [J].

CARASSO, A .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1982, 42 (03) :558-574

[4]

Das S, 2012, SPRINGERBR APPL SCI, P1, DOI 10.1007/978-3-642-23117-9

[5] APPROXIMATIONS FOR A CAUCHY-PROBLEM FOR THE HEAT-EQUATION [J].

ELDEN, L .

INVERSE PROBLEMS, 1987, 3 (02) :263-273

[6]

ELDEN L, 1995, SIAM PROC S, P130

[7]

Elden L, 1987, INVERSE ILL POSED PR, V4, P345

[8]

Fu CL, 2003, J COMPUT APPL MATH, V150, P143, DOI 10.1016/S0377-0427(02)00657-X

[9] A MOLLIFIED SPACE-MARCHING FINITE-DIFFERENCE ALGORITHM FOR THE 2-DIMENSIONAL INVERSE HEAT-CONDUCTION PROBLEM WITH SLAB SYMMETRY [J].

GUO, L ;

MURIO, D .

INVERSE PROBLEMS, 1991, 7 (02) :247-259

[10] Two new regularization methods for solving sideways heat equation [J].

Huy Tuan Nguyen ;

Vu Cam Hoan Luu .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2015, :1-17

← 1 2 3 4 5 →