Determination of an Unknown Time-dependent Heat Source from A Nonlocal Measurement by Finite Difference Method  

作　　者：Ze-wen WANG Zhou-sheng RUAN He-lu HUANG Shu-fang QIU 

机构地区：[1]School of Science,East China University of Technology,Nanchang 330013,China [2]Institute of Science and Engineering Computing,East China University of Technology,Nanchang 330013,China

出　　处：《Acta Mathematicae Applicatae Sinica》2020年第1期151-165,共15页应用数学学报（英文版）

基　　金：supported by National Natural Science Foundation of China(11561003,11661004,11761007);Natural Science Foundation of Jiangxi Province(20161BAB201034);Foundation of Academic and Technical Leaders Program for Major Subjects in Jiangxi Province(20172BCB22019)。

摘　　要：In this paper,we consider an inverse time-dependent source problem of heat conduction equation.Firstly,the ill-posedness and conditional stability of this inverse source problem is analyzed.Then,a finite difference inversion method is proposed for reconstructing the time-dependent source from a nonlocal measurement.The existence and uniqueness of the finite difference inverse solutions are rigorously analyzed,and the convergence is proved.Combined with the mollification method,the proposed finite difference inversion method can obtain more stable reconstructions from the nonlocal data with noise.Finally,numerical examples are given to illustrate the efficiency and convergence of the proposed finite difference inversion method.

关 键 词：INVERSE source PROBLEM ILL-POSED PROBLEM finite DIFFERENCE heat equation mollification 

分 类 号：TK124[动力工程及工程热物理—工程热物理] O241.3[动力工程及工程热物理—热能工程]