Determination temperature of a backward heat equation with time-dependent coefficients

被引：6

作者：

Nguyen Huy Tuan ^{[1
]}

Ngo Van Hoa ^{[1
]}

机构：

[1] Ton Duc Thang Univ, Div Appl Math, Ho Chi Minh City, Vietnam

来源：

MATHEMATICA SLOVACA | 2012年 / 62卷 / 05期

关键词：

backward heat problem; Ill-posed problem; nonhomogeneous heat; contraction principle; ILL-POSED PROBLEMS; FOURIER REGULARIZATION; CONDUCTION PROBLEM; ERROR ESTIMATE; STABILITY; APPROXIMATION; SPACE;

D O I：

10.2478/s12175-012-0056-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce the truncation method for solving a backward heat conduction problem with time-dependent coefficients. For this method, we give the stability analysis with new error estimates. Meanwhile, we investigate the roles of regularization parameters in these two methods. These estimates prove that our method is effective.

引用

页码：937 / 948

页数：12

共 26 条

[1] Structural stability for ill-posed problems in Banach space [J].

Ames, KA ;

Hughes, RJ .

SEMIGROUP FORUM, 2005, 70 (01) :127-145

[2]

[Anonymous], 1997, Current developments in mathematics

[3] A spectral method for solving the sideways heat equation [J].

Berntsson, F .

INVERSE PROBLEMS, 1999, 15 (04) :891-906

[4]

Clark G., 1994, Electronic Journal of Differential Equations, V1994, P1

[5] A modified quasi-boundary value method for ill-posed problems [J].

Denche, M ;

Bessila, K .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 301 (02) :419-426

[6] 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

[7] APPROXIMATION OF CERTAIN PARABOLIC EQUATIONS BACKWARD IN TIME BY SOBOLEV EQUATIONS [J].

EWING, RE .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1975, 6 (02) :283-294

[8] Numerical approximation of solution of nonhomogeneous backward heat conduction problem in bounded region [J].

Feng, Xiao-Li ;

Qian, Zhi ;

Fu, Chu-Li .

MATHEMATICS AND COMPUTERS IN SIMULATION, 2008, 79 (02) :177-188

[9] Fourier regularization for a backward heat equation [J].

Fu, Chu-Li ;

Xiong, Xiang-Tuan ;

Qian, Zhi .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 331 (01) :472-480

[10] Simplified Tikhonov and Fourier regularization methods on a general sideways parabolic equation [J].

Fu, CL .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2004, 167 (02) :449-463

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