Two Regularization Methods Simultaneous Determination of Initial Value and the Source Term of the Heat Conduction Problem

Xue-Juan Ren, Cheng-Bo Jin

In this paper, we investigate the inverse problem of determining a heat source and initial temperature simultaneously in a parabolic equation. Since, it is an ill-posed problem, we use the mollification method to solve  source and  use the modified method to solve initial value. And we obtain an optimal error estimate from an a priori parameter choice rule. Finally, two examples show that the proposed method is effective and efficient.