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

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.