A Restrained Optimal Perturbation Method for Solving the Inverse Problem in Reverse Process of Convection Diffusion Equation

摘要

In this paper, a new approach of the restrained optimal perturbation method is firstly proposed to study the inverse problem in the reverse process of the one-dimensional convection diffusion equation, the idea of this method is brand new that in search for the optimal perturbation value by the given initial estimate, for determining the initial distribution based on the overspecified data, and the initial estimates plus optimal perturbation value can be treated as the final initial distribution, in order to overcome the ill-posedness of this problem, a regularization term is introduced in the objective functional. Numerical examples will be given, and the results show that our method is effective.