西北师范大学学报（自然科学版）2024，Vol.60Issue(2)：26-28,3.DOI:10.16783/j.cnki.nwnuz.2024.02.005
热传导方程Robin系数反问题解的唯一性及正则化解的存在性
Uniqueness of solution to inverse problem for the Robin coefficient in heat conduction equation and existence of its regularized solution
摘要
Abstract
The Robin coefficient characterizes the heat exchange on the edge of the heat conduction region in the heat conduction model,which is a very important parameter.This article discussed the inversion problem of the Robin coefficient in the heat conduction model based on temperature measurements during a certain period of time.Firstly,the uniqueness result of the solution to the inverse problem was given under certain conditions of boundary and measured values.Then,based on Tikhonov's regularization idea,the objective functional was constructed,and the inverse problem was transformed into finding the minimum of the objective functional,and the existence of minimizer was proved.关键词
热传导方程/Robin系数/反问题/唯一性/极小元Key words
heat conduction equation/Robin coefficient/inverse problem/uniqueness/minimizer分类
数理科学引用本文复制引用
王兵贤,徐梅,张玲萍..热传导方程Robin系数反问题解的唯一性及正则化解的存在性[J].西北师范大学学报（自然科学版）,2024,60(2):26-28,3.基金项目
国家自然科学基金资助项目(11501236) （11501236）
江苏省高校自然科学基金面上项目(18kJD110002) （18kJD110002）
淮阴师范学院博士启动基金项目(31WBX00) （31WBX00）
