Identifying a Space-Dependent Source Term and the Initial Value in a Time Fractional Diffusion-Wave Equation

Abstract

This paper is focused on the inverse problem of identifying the space-dependent source function and initial value of the time fractional nonhomogeneous diffusion-wave equation from noisy final time measured data in a multi-dimensional case. A mollification regularization method based on a bilateral exponential kernel is presented to solve the ill-posedness of the problem for the first time. Error estimates are obtained with an a priori strategy and an a posteriori choice rule to find the regularization parameter. Numerical experiments of interest show that our proposed method is effective and robust with respect to the perturbation noise in the data.

Keywords

• ill-posed problem
• inverse spatial source problem
• mollification method
• error estimate
• bilateral exponential kernel