SIMULTANEOUS INVERSION OF THE SOURCE TERM AND INITIAL VALUE OF THE MULTI-TERM TIME FRACTIONAL SLOW DIFFUSION EQUATION

In this paper, the inverse problem of simultaneously identifying the source term and initial value for the multi-term time fractional diffusion equation is studied. We prove this problem is ill-posed, i.e. the solution (if it exists) does not continuous depend on measurement data. A standard Tikhonov regularization method is proposed to solve the inverse problem. In the case of a-priori and a-posteriori, we derive the error estimates between the exact solution and the regularized solution. Finally, we provide two examples to show the validity of the proposed method.