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OA北大核心CSTPCD

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.