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

作　　者：王泽文 王梓鉴 陈国林 邱淑芳 WANG Zewen;WANG Zijian;CHEN Guolin;QIU Shufang(Department of Basic Courses,Guangzhou Maritime University,Guangzhou 510725,China;School of Science,East China University of Technology,Nanchang 330013,China;College of Life Science,Gannan Normal University,Ganzhou 341000,China;Department of Basic Courses,Gandong University,Fuzhou 344000,China)

机构地区：[1]广州航海学院基础教学部,广东广州510725 [2]东华理工大学理学院,江西南昌330013 [3]赣南师范大学生命科学学院,江西赣州341000 [4]赣东学院基础部,江西抚州340000

出　　处：《山西大学学报（自然科学版）》2024年第2期302-312,共11页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(12261004;12171248;11961002);江西省自然科学基金(20212ACB201001);东华理工大学研究生创新项目(DHYC-2022);广州航海学院(广州交通大学(筹))科研启动项目。

摘　　要：研究了有界域中热传导方程源项和初始分布同时反演问题。通过热传导定解问题的特征系统,结合分离变量的思想方法,构造了一种能同时重建热传导方程源项和初始分布的Tikhonov正则化方法,证明了正则化解的收敛性,给出了正则化参数选取的后验策略及其正则化解的误差估计。最后,对提出的正则化方法进行了数值模拟,研究结果表明正则化方法是有效的。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 variables,the Tikhonov regularization method that can simultaneously reconstruct the source term and initial distribution of heat conduction equation,is constructed.The convergence of the regularization solution is proved,and the posterior strategy of regularization parameter selection is given with error estimation of the regularization solutions.Finally,numerical simulations for the proposed regularization 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 

分 类 号：O175.26[理学—数学]