应用数学和力学2025，Vol.46Issue(4)：505-518,14.DOI:10.21656/1000-0887.450029
重构具有Wentzell边界条件的抛物型方程的热源
Reconstruction of Heat Sources for Parabolic Equations With Wentzell Boundary Conditions
摘要
Abstract
The inverse problem of reconstructing spatially related source terms in parabolic heat conduction e-quations was studied under the Wentzell boundary conditions and with the terminal temperature measurements.This study has important applications in determining the source terms in heat conduction engineering problems,and the difficulty lies in the handling of the Wentzell boundary conditions.Based on the divergence theorem,the boundary conditions were combined with parabolic equations.The extremum principle was proved different-ly under various boundary conditions.Due to the ill-posedness of the original problem,based on the framework of the optimal control theory,the original problem was optimized,and the existence and necessary conditions for the regularization solution were established.Furthermore,under the validness of the extremum principle,the uniqueness and stability of the regularization solution were proved.关键词
反源问题/Wentzell边界条件/最优控制/散度定理Key words
inverse source problem/Wentzell boundary condition/optimal control/divergence theorem分类
数学引用本文复制引用
伊海鸿,杨柳,田瑜..重构具有Wentzell边界条件的抛物型方程的热源[J].应用数学和力学,2025,46(4):505-518,14.基金项目
国家自然科学基金(61663018 （）
11961042) （）
甘肃省自然科学基金(25JRRA163 （）
25JRRA952) （）
