单边退化抛物方程反问题的收敛性分析  

Convergence Analysis of Inverse Problems forOne-Sided Degenerate Parabolic Equations

作　　者：陈嘉琪 杨柳[1] CHEN Jiaqi;YANG Liu(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,兰州730070

出　　处：《吉林大学学报（理学版）》2024年第6期1308-1316,共9页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:61663018,11961042);甘肃省自然科学基金(批准号:22JR5RA341).

摘　　要：考虑利用已知终端观测数据进行单边退化抛物型方程辐射系数反演的收敛性分析问题.首先,对单边退化抛物型方程,需满足Fichera条件以确保问题的可解性;其次,将原反问题转化为一个最优控制问题,通过最优控制方法找到辐射系数的最优解;最后,结合Gateaux导数并引入新的源条件,证明最优解的收敛性.We considered the convergence analysis problem of the inversion of the radiation coefficient of a one-sided degenerate parabolic equation by using known terminal observation data.Firstly,it was necessary to satisfy the Fichera condition for the one-sided degenerate parabolic equation to ensure the solvability of the problem.Secondly,we tra nsformed the original inverse problem into an optimal control problem and found the optimal solution for the radiation coefficient through optimal control methods.Finally,by combining the G teaux derivative and introducing new source conditions,we proved the convergence of the optimal solution.

关 键 词：反问题 单边退化抛物方程 Fichera条件 Gateaux导数 收敛性 

分 类 号：O175.9[理学—数学]