Optimal Error Bound in a Sobolev Space of Regularized Approximation Solutions for a Sideways Parabolic Equation
-
摘要: 逆热传导问题(IHCP)是严重不适定问题，即问题的解(如果存在)不连续依赖于数据．但目前关于逆热传导问题的已有结果主要是针对标准逆热传导问题．文中给出了出现在实际问题中的一个抛物型方程侧边值问题,即一个含有对流项的非标准型逆热传导问题的正则逼近解一类Sobolev空间中的最优误差界．
-
关键词:
- 逆热传导问题 /
- 不适定问题 /
- 抛物型方程侧边值问题 /
- 正则化方法 /
- 最优误差界
Abstract: The inverse heat conduction problem(IHCP)is severely ill-posed problem in the sense that the solution(if it exists)does not depend continuously on the data.But now the results on inverse heat conduction problem are mainly devoted to the standard inverse heat conduction problem.Some optimal error bounds in a sobolev spaceof regularized approximation solutions for a sideways parabolic equation,i.e.,a non-standard inverse heat conduction problem with convection term which appears in some applied subject are given. -
[1] Beck J V,Blackwell B,Clair C R.Inverse Heat Conduction: Ⅰ[KG-*4]. ll-Posed Problem[M].New York:Wiley,1985，1—8，108—110. [2] Carrasso A.Determining surface temperature from interior observations[J].SIAM Journal of Applied Mathematics,1982,42(3):558—574. doi: 10.1137/0142040 [3] Beck J V.Nonlinear estimation applied to the nonlinear inverse heat conduction problem[J].International Journal of Heat and Mass Transfer,1970,13(4):703—716. doi: 10.1016/0017-9310(70)90044-X [4] FU Chu-li,ZHU You-bin,QIU Chun-yu.Wavelet regularization for an inverse heat conduction problem[J].Journal of Mathematical Analysis and Applications,2003,288(1):212—222. doi: 10.1016/j.jmaa.2003.08.003 [5] XIONG Xiang-tuan,FU Chu-li,LI Hong-fang.Central difference schemes in time amd error estimate on a non-standard inverse heat conduction problem[J].Applied Mathematics and Computation,2004,157(1):77—91. doi: 10.1016/j.amc.2003.08.028 [6] FU Chu-li,XIONG Xiang-tuan,LI Hong-fang,et al.Wavelet and spectralregularized methods for a sideways parabolic equation[J].Applied Mathematics and Computation,2005,160(3):881—908. doi: 10.1016/j.amc.2003.12.007 [7] 邱春雨,陶建红，傅初黎.一维非标准型逆热传导问题的Fourier正则化方法[J].兰州大学学报，2002,38(1):1—5. [8] Tautenhahn U.Optimal stable approximations for the sideways heat equation[J].Journal of Inverse and Ⅰ[KG-*4]. ll-Posed Problems,1997,5(3):287—307. [9] Tautenhahn U.Optimality for ill-posed problems under general source conditions[J].Numerical Functional Analysis and Optimization,1998,19(3/4):377—398. doi: 10.1080/01630569808816834 -
计量
- 文章访问数: 2575
- HTML全文浏览量: 103
- PDF下载量: 758
- 被引次数: 0
下载:
渝公网安备50010802005915号