宁夏大学学报（自然科学版）2024，Vol.45Issue(2)：97-106,10.
具Robin条件的高维扩散方程反问题正则化算法
Regularization Algorithms for Inverse Problems of High-dimensional Diffusion Equations with Robin Boundary Conditions
摘要
Abstract
The simultaneous identification of the initial heat field and the heat source is a class of inverse prob-lems in heat conduction equations.By utilizing temperature measurements at two fixed moments,an improved regularization method is proposed to stably determine both the initial temperature and heat source terms.A sta-bilization algorithm is thus obtained.Strategies for selecting regularization parameters and error estimates for the regularization solutions are provided.Additionally,pre-processing is performed on the measurement data with noise interference to improve accuracy.Numerical experiments verify the effectiveness of the algorithm.关键词
高维热传导方程/Robin边界条件/改进正则化方法/数据预处理/误差估计Key words
high-dimensional heat conduction equations/Robin boundary conditions/improved regularization methods/data pre-processing/error estimation分类
数理科学引用本文复制引用
郭琴,徐定华..具Robin条件的高维扩散方程反问题正则化算法[J].宁夏大学学报（自然科学版）,2024,45(2):97-106,10.基金项目
国家自然科学基金资助项目(12371428,11871435) （12371428,11871435）
