山西大学学报（自然科学版）2024，Vol.47Issue(2)：302-312,11.DOI:10.13451/j.sxu.ns.2023013
热源和初始分布同时反演的Tikhonov正则化方法
Tikhonov Regularization Method for Simultaneous Reconstruction of Heat Conduction Source and Initial Distribution
摘要
Abstract
The problem of simultaneous inversion of the source term and initial distribution of heat conduction equation in bounded domains is studied.Through the characteristic system of the heat conduction problem,combined with the idea of separating vari-ables,the Tikhonov regularization method that can simultaneously reconstruct the source term and initial distribution of heat conduc-tion equation,is constructed.The convergence of the regularization solution is proved,and the posterior strategy of regularization pa-rameter selection is given with error estimation of the regularization solutions.Finally,numerical simulations for the proposed regu-larization method are carried out,and the results show that the regularization method is effective.关键词
热传导方程/反问题/正则化方法/源项/初始分布Key words
heat conduction equation/inverse problem/regularization method/source term/initial distribution分类
数理科学引用本文复制引用
王泽文,王梓鉴,陈国林,邱淑芳..热源和初始分布同时反演的Tikhonov正则化方法[J].山西大学学报（自然科学版）,2024,47(2):302-312,11.基金项目
国家自然科学基金(12261004 （）
12171248 （）
11961002) （）
江西省自然科学基金(20212ACB201001) （20212ACB201001）
东华理工大学研究生创新项目(DHYC-2022) （DHYC-2022）
广州航海学院(广州交通大学(筹))科研启动项目 （广州交通大学(筹）
