应用数学和力学2025，Vol.46Issue(7)：904-915,12.DOI:10.21656/1000-0887.450221
从终端数据识别生物传热过程中空间热源的反问题
The Inverse Problem of Identifying Spatial Heat Sources in Biological Heat Transfer Processes From Terminal Data
摘要
Abstract
The inverse problem of reconstructing spatial heat sources in the thermal wave diffusion model for biological organisms,was Investigated.Unlike traditional parabolic models for biological heat transfer,this work was focused on a more complex and practical hyperbolic model,particularly suitable for biomedical engi-neering applications.Firstly,the optimal control theory was employed,and the inverse problem was formulated as an optimal control problem.To address the challenge of non-uniqueness in the optimal solution due to the non-differentiability of total variation functions,a carefully designed and polished total variation regularization term was introduced.Subsequently,the existence of the optimal solution and its necessary conditions were thoroughly discussed.Secondly,under the assumption of a small terminal time,the uniqueness and stability of the optimal solution were proven with the Sobolev embedding theory.Last,a gradient-based optimization algo-rithm was developed based on these necessary conditions,and its effectiveness was demonstrated through sev-eral numerical examples.关键词
反问题/生物传热/空间热源/梯度型算法/数值算例Key words
inverse problem/biological heat transfer/space heat source/gradient algorithm/numerical example分类
数理科学引用本文复制引用
铁旭玮,杨柳..从终端数据识别生物传热过程中空间热源的反问题[J].应用数学和力学,2025,46(7):904-915,12.基金项目
国家自然科学基金(61663018 （）
11961042) （）
甘肃省自然科学基金(22JR5RA341) （22JR5RA341）
