识别热传导过程中抛物型方程源项的正则化方法
Regularization Method for Identifying the Source Term in Parabolic Equations during Heat Conduction Processes
尚梦莹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
利用最终测量温度重构了热传导过程中抛物型热方程中的热源,用全变差正则化方法将反问题转化为优化问题.通过引入一个磨光全变差的正则化项导出了目标泛函存在最小值的必要条件,利用最小值存在的必要条件证明了极小元的唯一性和稳定性.
Abstract
The heat source in the parabolic heat equation during the heat conduction process is reconstructed using the final measured temperature,and the inverse problem is transformed into an optimization problem using the total variation regularization method.The necessary condition for the existence of the minimum value of the objective functional is derived by introducing a polished total variation regularization term.The necessary conditions for the existence of the minimum value are used to prove the uniqueness and stability of the minimal element.
关键词
反问题/源项/全变差/必要条件Key words
inverse problem/source term/necessary condition/total variation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