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一个非标准逆热传导问题的具有对数稳定性的Fourier正则化方法 被引量：3

A Fourier Regularization Method with Logarithmic Stability for a Non-standard Inverse Heat Conduction Problem
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摘要 逆热传导问题是严重不适定问题,即问题的解(如果存在)将不连续依赖于测量数据,使其数值计算非常困难.但最近20 年来人们主要关注标准的逆热传导问题而对非标准情形研究较少.本文给出了一个非标准逆热传导问题的具有对数稳定性的Fourier正则化方法,恢复了解对数据的连续依赖性. Inverse heat conduction problems (IHCP) are severely i ll -posed problems.The solution,if it exists,does not depend continuously on the d ata such that its numerical computation is very difficult.But now the results av ailable in the literature on IHCP are mainly devoted to the standard case.In thi s paper a new Fourier regularization method with logarithmic stability for a non -standard IHCP is provided.
作者 傅初黎 赵华 钱志
机构地区 兰州大学数学与统计学院
出处 《应用数学》 CSCD 北大核心 2005年第2期238-243,共6页 Mathematica Applicata
基金 国家自然科学基金资助项目(10271050) 甘肃省自然科学基金资助课题(ZS021 A25 001 Z)
关键词 逆热传导问题 不适定问题 正则化 误差估计 对数稳定性 Inverse heat conduction problem Ill-posed problem Regul arization Error estimate Logarithmic stability
分类号 O175 [理学—基础数学]
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参考文献9

  • 1Beck J V, Blackwell B, Clair S R. Inverse Heat Conduction: Ill-posed Problem[M]. New York: Wiley.1985.
  • 2Carasso A. Determining surface temperature from interior observations[J].SIAM J. Appl. Math., 1982,42:558-574.
  • 3Elden L. Numerical solution of the sideways heat equation by difference approximation in time[J]. Inverse Problems, 1995,11:913 -923.
  • 4Elden L,Berntsson F,Reginska T. Wavelet and Fourier methods for solving the sideways heat equation[J]. SIAM J. Sci. Comp. ,2000,21(6) :2187-2205.
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  • 6Fu Chuli,Qiu Chunyu. Wavelet and error estimation of surface heat flux[J].J. Comp. Appl. Math. ,2003,150:143-155.
  • 7Qiu Chunyu,Fu Chuli,Zhu Youbi. Wavelests and regularization of the sideways heat equation[J]. Computers and Mathematics with Applications, 2003,46 : 821 - 829.
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同被引文献15

  • 1王义龙,贺永春,杨君慧.一个抛物型方程逆问题的Fourier和小波正则化方法[J].榆林学院学报,2006,16(2):1-4. 被引量：2
  • 2王海龙,张选德.一个非标准逆热传导方程的正则化方法[J].固原师专学报,2006,27(6):27-30. 被引量：1
  • 3Carasso A S. Determining surface temperatures from interior observations. SIAM J Appl Math, 1982, 42: 558 574.
  • 4RegiUnska T. Sideways heat equation and wavelets. J Comput Appl Math, 1995, 63:239-264.
  • 5Regi'nska T, Eld'en L. Solving the sideways heat equation by a Wavelet-Galerkin method. Inverse Prob- lems. 1997:1093-1106.
  • 6EldUen L, Bernfsson F, RegiUnska T. Wavelets and Fourier methods for solving the sideways heat equation. SIAM J Sci Comput, 20001 21(6): 2187-2205.
  • 7Fu Chuli, Qiu Chunyu. Wavelet and error estimation of surface heat flux. J Comput Appl Math, 2003, 150:143 155.
  • 8Shidfar A, Neisy A. A two-dimensional inverse heat conduction problem for estimating heat flux. Far East J Appl, 2003, 10(2): 145 150.
  • 9Daubechies I. Ten Lectures on Wavelets. CBMS-NSF Regional Conference Series in Applied Mathematics. Philadelphia: SIAM, 1992.
  • 10杨帆,万诗敏,李敦刚.含对流项抛物方程的热源识别的拟逆正则化方法[J].兰州理工大学学报,2009,35(4):146-148. 被引量：10

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应用数学
2005年 第2期

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