含对流项逆热传导问题的迭代正则化方法

Iterative Regularization Method for Inverse Heat Conduction Problem with Convection Term

本文考虑一个非标准的逆热传导问题,该问题在Hadamard[1]意义下是严重不适定的.我们首先通过Fourier变换导出问题的解并给出问题的条件稳定性,之后采用一种改进的迭代正则化方法构造出问题的正则近似解,分别在一种先验和一种后验参数选取准则下得到了正则解与精确解之间的H9lder型误差估计.

A nonstandard inverse heat conduction problem is discussed,which is ill posed in the sense of Hadamard.First,the solution of the problem by Fourier transform is derived and the conditional stability of the problem given,then an improved iterative regularization method is used to construct the regularized approximate solution of the problem.The H9 lder type error estimation between the approximate solution and the exact solution are obtained under an a-priori and an a-posteriori regularization parameter choice rule,respectively.