Inverse Source Problem For A Time Fractional Diffusion Wave Equation

In this paper, we consider an inverse source problem for a time-fractional diffusion wave equation in a bounded domain. That is to determine a space-dependent source term in a time-fractional diffusion wave equation from a noisy final data. Since the inverse problem is ill-posed, we use the Tikhonov regularization method to solve the inverse source problem. Furthermore we obtain two kinds of convergence rates under an a priori regularization parameter choice rule and an a posteriori regularization parameter choice rule . Numerical examples in one-dimensional and two-dimensional cases are provided to show the effectiveness and stability of the proposed method.