四川大学学报（自然科学版）2024，Vol.61Issue(1)：15-24,10.DOI:10.19907/j.0490-6756.2024.011003
用Tikhonov正则化方法同时反演对流扩散方程的对流速度和源函数
Simultaneously inverting the convection velocity and source function of convection-diffusion equations by using the Tikhonov regularization method
摘要
Abstract
In this paper,given additionally two observation data,the inverse problem of simultaneously inverting the convection velocity and source function of the convection diffusion equations is studied.The original problem belongs to a class of convection-diffusion equations with non-zero initial value.First,by transforming the information of the initial value into a source function and then combining it with the source function,we transform the original problem into a convection-diffusion problem with homogeneous conditions.Further,to handle the ill-posedness of the new problem,we construct the cor-responding minimization objective functional by using the Tikhonov regularization method,and the ex-istence and necessary conditions for the optimal solution are discussed.Finally,for the special case of small terminal time,the uniqueness and stability of the optimal solution are obtained.关键词
对流扩散方程/反问题/源函数/Tikhonov正则化方法Key words
Convection-diffusion equation/Inverse problem/Source function/Tikhonov regularization method分类
数理科学引用本文复制引用
周子融,杨柳,王清艳..用Tikhonov正则化方法同时反演对流扩散方程的对流速度和源函数[J].四川大学学报（自然科学版）,2024,61(1):15-24,10.基金项目
国家自然科学基金(61663018,11961042) （61663018,11961042）
甘肃省自然科学基金(22JR5RA341) （22JR5RA341）
