变系数导热方程的Robin系数反演问题  

Robin Coefficient Inversion Problem of Variable Coefficient Heat Conduction Equation

作　　者：刘翻丽 解金鑫 杨涛[2] LIU FANLI;XIE JINXIN;YANG TAO(Shanxi Normal University Yang Ling Experimental Middle School,Xianyang 712000,China;Department of Mathematics,Lanzhou Jiao tong University,Lanzhou 730070,China)

机构地区：[1]陕西师范大学杨凌实验中学,咸阳712000 [2]兰州交通大学数理学院,兰州730070

出　　处：《应用数学学报》2021年第4期574-588,共15页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10571169,10731010);国家重点基础研究发展计划(2007CB814902);湖北省高等学校优秀中青年科技创新团队项目经费(03BA85)资助项目。

摘　　要：本文研究基于非局部边界附加条件下,一类变系数抛物型方程的Robin系数确定问题,这里的Robin系数仅与时间相关.首先给出了变分公式,并利用变分公式证明了解的唯一性,其次给出了时间离散模型,基于线性离散化的变分形式,导出了一系列先验估计,证明了弱解的存在性,并对其进行了误差分析.In this paper,based on the nonlocal boundary conditions,the Robin coefficient of one kind of parabolic equation with variable coefficients is determined,the Robin coefficient is only related to time.Here the first variational formula is given,the uniqueness is proved by using the variational formula,second time discrete model is given,based on linear variational form of discretization,a series of a prior estimate are derived,the existence of weak solutions is proved,and it’s error is analyzed.

关 键 词：唯一性 弱解存在性 误差分析 Robin系数 

分 类 号：O175.26[理学—数学]