热传导方程的非线性传热定律识别问题
Identification of nonlinear heat transfer law of heat conduction equation
杜乐 1杨柳 1张涛1
作者信息
- 1. 兰州交通大学数理学院,甘肃 兰州 730070
- 折叠
摘要
考虑利用边界控制识别热传导方程中与温度相关的传热系数问题.基于最优控制理论,将热传导方程参数反演问题转化为变分问题,进而讨论了极小值的存在性以及必要条件,最终利用能量模估计的方法,在假设终端时刻较小的情况下,证得极小值的唯一性和稳定性.
Abstract
The identification of temperature-dependent heat transfer coefficients in heat conduction equations by boundary control is considered.Based on the optimal control theory,the general heat conduction equation parameter inversion problem is transformed into a variational problem,and then the existence and necessary conditions of the minimum value are discussed.Finally,by using the energy norm estimation method,the uniqueness and stability of the minimum value are proved under the assumption that the terminal time is small.
关键词
热传导方程/反问题/非线性传热定律/非线性边界/最优控制Key words
heat conduction equation/inverse problem/nonlinear heat transfer law/nonlinear boundary/optimal control引用本文复制引用
基金项目
国家自然科学基金资助项目(61663018)
国家自然科学基金资助项目(11961042)
甘肃省自然科学基金资助项目(22JR5RA341)
出版年
2024
NETL
NSTL
万方数据