Numerical simulation for an inverse source problem in a degenerate parabolic equation

被引：10

作者：

Rao, Xiao-Bo ^{[1
]}

Wang, Yu-Xin ^{[1
]}

Qian, Kun ^{[1
]}

Deng, Zui-Cha ^{[1
]}

Yang, Liu ^{[1
]}

机构：

[1] Lanzhou Jiaotong Univ, Dept Math, Lanzhou 730070, Gansu, Peoples R China

来源：

APPLIED MATHEMATICAL MODELLING | 2015年 / 39卷 / 23-24期

关键词：

Inverse problem; Heat source; Uniqueness; Difference scheme; Landweber iteration; Numerical results; FINAL MEASUREMENT DATA; DEPENDENT HEAT-SOURCE; CAUCHY-PROBLEM; COEFFICIENT; VOLATILITY; 1ST-ORDER; ALGORITHM; SPACE;

D O I：

10.1016/j.apm.2015.03.016

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

This paper deals with an inverse problem of identifying the source coefficient in degenerate parabolic equations. On the basis of extremum principle, the uniqueness of the proposed problem is obtained. The difference scheme for the direct problem is got by using the finite volume method and the corresponding stability is also proved. An iteration scheme of the Landweber type is applied to handle the numerical solution. In the end, several numerical experiments are performed to test the validity of the scheme. The numerical results show that the method is stable and the unknown function is recovered very well when iterative parameter a and iterative times are matching appropriately. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：7537 / 7553

页数：17

共 32 条

[11]

Engl Heinz Werner, 1996, REGULARIZATION INVER, V375

[12] INVERSE PARABOLIC PROBLEMS WITH THE FINAL OVERDETERMINATION [J].

ISAKOV, V .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1991, 44 (02) :185-209

[13]

Isakov V., 2006, INVERSE PROBLEMS PAR, V127

[14]

Isakov V., 1997, INVERSE PROBL, V13, P7

[15] A new well-posed algorithm to recover implied local volatility [J].

Jiang, LS ;

Chen, QH ;

Wang, LJ ;

Zhang, JE .

QUANTITATIVE FINANCE, 2003, 3 (06) :451-457

[16] Identifying the volatility of underlying assets from option prices [J].

Jiang, LS ;

Tao, YS .

INVERSE PROBLEMS, 2001, 17 (01) :137-155

[17] Determination of a spacewise dependent heat source [J].

Johansson, Tomas ;

Lesnic, Daniel .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 209 (01) :66-80

[18] Numerical identifications of parameters in parabolic systems [J].

Keung, YL ;

Zou, J .

INVERSE PROBLEMS, 1998, 14 (01) :83-100

[19]

Kindermann S., 2000, INVERSE PROBL, V16, P665

[20] OPTIMAL-CONTROL FOR DEGENERATE PARABOLIC EQUATIONS WITH LOGISTIC GROWTH [J].

LENHART, SM ;

YONG, JM .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1995, 25 (07) :681-698

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