IDENTIFYING AN UNKNOWN SOURCE IN SPACE-FRACTIONAL DIFFUSION EQUATION

被引：14
作者：
Yang, Fan [1 ,2 ]
Fu, Chuli [2 ]
Li, Xiaoxiao [1 ]
机构：
[1] Lanzhou Univ Technol, Sch Sci, Lanzhou 730050, Peoples R China
[2] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China
来源：
ACTA MATHEMATICA SCIENTIA | 2014年 / 34卷 / 04期
基金：
中国国家自然科学基金;
关键词：
spatial-dependent heat source; space-fractional diffusion equation; generalized Tikhonov regularization; A posteriori parameter choice; error estimate; DEPENDENT HEAT-SOURCE; FINITE-DIFFERENCE APPROXIMATIONS; TIKHONOV REGULARIZATION METHOD; INVERSE SOURCE PROBLEM; CONDITIONAL STABILITY; ANOMALOUS DIFFUSION; SOURCE-TERM; RANDOM-WALK; DYNAMICS;
D O I：
10.1016/S0252-9602(14)60065-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we identify a space-dependent source for a fractional diffusion equation. This problem is ill-posed, i.e., the solution (if it exists) does not depend continuously on the data. The generalized Tikhonov regularization method is proposed to solve this problem. An a priori error estimate between the exact solution and its regularized approximation is obtained. Moreover, an a posteriori parameter choice rule is proposed and a stable error estimate is also obtained. Numerical examples are presented to illustrate the validity and effectiveness of this method.
引用
收藏
页码：1012 / 1024
页数：13
相关论文
共 36 条
[1]   The method of fundamental solutions for the inverse space-dependent heat source problem [J].
Ahmadabadi, M. Nili ;
Arab, M. ;
Ghaini, F. M. Maalek .
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2009, 33 (10) :1231-1235
[2]   The fractional-order governing equation of Levy motion [J].
Benson, DA ;
Wheatcraft, SW ;
Meerschaert, MM .
WATER RESOURCES RESEARCH, 2000, 36 (06) :1413-1423
[3]   Structural identification of an unknown source term in a heat equation [J].
Cannon, JR ;
DuChateau, P .
INVERSE PROBLEMS, 1998, 14 (03) :535-551
[4]   Wavelet and Fourier methods for solving the sideways heat equation [J].
Eldén, L ;
Berntsson, F ;
Reginska, T .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2000, 21 (06) :2187-2205
[5]  
Engl H. W., 1996, REGULARIZATION INVER
[6]   Numerical approximation of a time dependent, nonlinear, space-fractional diffusion equation [J].
Ervin, Vincent J. ;
Heuer, Norbert ;
Roop, John Paul .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2007, 45 (02) :572-591
[7]   The boundary-element method for the determination of a heat source dependent on one variable [J].
Farcas, Adrian ;
Lesnic, Daniel .
JOURNAL OF ENGINEERING MATHEMATICS, 2006, 54 (04) :375-388
[8]   Discrete random walk models for space-time fractional diffusion [J].
Gorenflo, R ;
Mainardi, F ;
Moretti, D ;
Pagnini, G ;
Paradisi, P .
CHEMICAL PHYSICS, 2002, 284 (1-2) :521-541
[9]   Data compatibility and conditional stability for an inverse source problem in the heat equation [J].
Li, GS .
APPLIED MATHEMATICS AND COMPUTATION, 2006, 173 (01) :566-581
[10]  
Li X., 2013, J APPL MATH, V2013, P1
1234