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

作　　者：尚梦莹 SHANG Mengying(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,甘肃兰州730070

出　　处：《新乡学院学报》2024年第9期10-13,21,共5页Journal of Xinxiang University

基　　金：国家自然科学基金资助项目(61663018,11961042);甘肃省自然科学基金资助项目(22JR5RA341)。

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。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 

分 类 号：O175[理学—数学]