非局部边界条件下的逆热传导问题

An Inverse Heat Conduction Problem under Nonlocal Boundary Conditions

研究了一类非局部边界条件下的逆热传导问题。由于问题的不适定性,需要额外的超定条件。先用分离变量法构造特征函数系统,再通过辅助谱理论和Fourier方法确定解的一般形式,通过级数收敛判别法和Schauder不动点定理证明解的存在性,最后利用估计证明解的唯一性和稳定性。同时,采用预测矫正型迭代法和Crank Nicoloson有限差分格式相结合的方法对反演问题进行数值分析,并讨论了数值算例。

A class of inverse heat conduction problem under nonlocal boundary conditions is studied.Since the inverse problem is ill-posed,the additional over-determined condition has been required.The characteristic function system is constructed by separating variables,and the general form of the solution is determined by the auxiliary spectral theory and Fourier method.The existence of the solution is proved by series convergence criterion and Schauder fixed point theorem,and the uniqueness and stability of the solution are proved by estimation.At the same time,the predictive correction iteration method and Crank-Nicoloson finite difference scheme are used to analyze the inversion problem,and numerical examples are discussed.