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

作　　者：王兵贤 徐梅[1] 张玲萍[1] WANG Bing-xian;XU Mei;ZHANG Ling-ping(School of Mathematics and Statistics,Huaiyin Normal University,Huaian 223300,Jiangsu,China)

机构地区：[1]淮阴师范学院数学与统计学院,江苏淮安223300

出　　处：《西北师范大学学报（自然科学版）》2024年第2期26-28,共3页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11501236);江苏省高校自然科学基金面上项目(18kJD110002);淮阴师范学院博士启动基金项目(31WBX00)。

摘　　要：Robin系数在热传导模型中刻画了热传导区域边界上的热交换,是一类非常重要的参数,本文基于某小时段温度测量值反演热传导模型中的Robin系数.首先,在边界值以及测量值满足一定的光滑性条件时,给出了反问题解的唯一性;其次,基于Tikhonov正则化思想,通过构造目标泛函将反问题转化为求目标泛函的极小值,并证明了泛函极小元的存在性.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 

分 类 号：O241.82[理学—计算数学]