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 fcuntion and then combining it with the original 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 corresponding minimization objective function by using the Tikhonov regularization method, and the existence and necessary conditions for the optimal solution of the new problem are discussed. Finally, for the special case of small terminal time, the uniqueness and stability of the optimal solution are obtained.
