Regularization Methods To The Identification Of Source Term In One Dimensional Heat Equation

In this paper, we study the identification of a source term in one dimensional heat equation, which is widely used in the identification of pollution sources. Due to the ill-posedness of the problem, the numerical calculation becomes very difficult.In the bounded domain case, we introduce the Ritz approximation method to restore the stability. Convergence results are given when the finite approximate spaces are specially choosed as eigenfunction space and Harr wavelet function space.In the unbounded case, we solve the problem with Fourier transform method first, then mollification method is applied to restore the stability. Convergence result is given.Additionally, several numerical examples are presented, which illustrate the efficiency of our proposed methods.