紧算子方程的不适定性分析及其在一维热传导反问题中的应用  

Ill-Posedness of Compact Operator Equation and Its Application in One-Dimensional Backward Heat Conduction Problem

作　　者：闵涛[1] 葛宁国[1] 张敏[1] 张帆[1] 

机构地区：[1]西安理工大学理学院,西安710054

出　　处：《应用泛函分析学报》2012年第2期140-146,共7页Acta Analysis Functionalis Applicata

基　　金：陕西省教育厅基金(08JK388)

摘　　要：对紧算子方程的不适定性进行了详细的分析,证明了紧算子方程奇异值分解定理,并以一维热传导方程反问题为例,将其转化为紧算子方程,讨论了求解此反问题的最优估计及进行了误差分析,数值模拟表明了理论分析与实际应用的一致性.The purpose of the paper is to discuss the ill-posedness and to prove the singular value decomposition theorem of compact operator equation.Then taking one-dimensional backward heat conduction problem for example,we translate it into compact operator equation and put forward an optimal estimate of which error analysis is also given for solving the ill-posed problem.Numerical simulation shows that the theoretical analysis is consistent with practical application.

关 键 词：紧算子 反问题 不适定 正则化 正则参数 

分 类 号：O177.1[理学—数学] O242.1[理学—基础数学]