On the Stability Estimation of Analytic Continuation for Potential Field

Xu Dinghua; Cheng Jin; Li Ming zhong

Volume 19 Issue 6

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Abstract

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Article Navigation > Applied Mathematics and Mechanics > 1998 > 19(6): 528-537

Xu Dinghua, Cheng Jin, Li Ming zhong. On the Stability Estimation of Analytic Continuation for Potential Field[J]. Applied Mathematics and Mechanics, 1998, 19(6): 528-537.

Citation:

Xu Dinghua, Cheng Jin, Li Ming zhong. On the Stability Estimation of Analytic Continuation for Potential Field[J]. Applied Mathematics and Mechanics, 1998, 19(6): 528-537.

Citation:

Xu Dinghua, Cheng Jin, Li Ming zhong. On the Stability Estimation of Analytic Continuation for Potential Field[J]. Applied Mathematics and Mechanics, 1998, 19(6): 528-537.

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On the Stability Estimation of Analytic Continuation for Potential Field

1.
P. O. Box 267, East China Geological Institute, Fuzhou, Jiangxi 344000, P. R. China;
2.
Department of Mathematics, Fudan University, Shanghai 200433, P. R. China;
3.
Department of Mathematics, Shanghai University, Shanghai 200072, P. R. China

Received Date: 1996-09-20
Publish Date: 1998-06-15

Abstract

Abstract

This paper discusses the stability of solutions to a class of Cauchy pro blems for Laplace equatio ns under two kinds of nonclassical circumstances. By means of conformal mapping and Tikhonov, Luan Wengui and Yamamo to. smethods for solving ill-posed problems respectively, the stability estimations of weighted Hlder type and logarithmic type, have been obtained accor dingly.
- Cauchy problems for Laplace equations,
- analytic continuation of potential field,
- ill-posed problems,
- stability estimation

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References(8)

References

[1]	L.Nirenberg,Uniqueness in Cauchy problems for differential equations with constant leading coefficients,Comm.Pure Appl.Math.,10(1)(1957),89-115.
[2]	栾文贵著,《地球物理中的反问题》,科学出版社(1989),32-65.
[3]	栾文贵,位场、波场和电磁场的延拓,中国科学(A辑),(9)(1985),824-839.
[4]	李明忠、候宗义、徐振远著,《椭圆型方程组理论和边值问题》,复旦大学出版社(1990),228-231.
[5]	程晋、徐定华,关于一类微分方程反问题的若干讨论,宁夏大学学报(自然科学版),17(1)(1996),74) 75.
[6]	A.N.Tikhonov and V.Y.Arsenin,Solutions of Ill-Posed Problems,V.H.Winston and Sons(1977),27) 32.
[7]	M.Yamamo to,Conditional stability in determination of force terms of heat equations in arectangle,Math.Comput.Modelling,18(1)(1993),79-88.
[8]	河田龙夫著,《Fourier分析》,周民强译,高等教育出版社(1982),108-112.

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