A Quasi-boundary Value Regularization Method For Solving The Source Term Identification Problem Of The Fractional Equation

This paper is devoted to identifying a space-dependent source term for a time fractional diffusion-wave equation in a bounded domain.By the series expression of the solution for the direct problem,the original problem can be transformed into a first kind of Fredholm integral equation.The uniqueness,ill-posedness and conditional stability of this space-dependent source term identification problem are considered.Then we propose a generalized quasi-boundary value regulariza-tion method to solve the space-dependent source term identification problem and also prove that the regularization problem is well-posed.Further,two kinds of convergence rates for the regularized solution can be proved by using an a priori and an a posteriori regularization parameter choice rule,respectively.Numerical examples in one-dimensional case and two-dimensional case are given to confirm our theoretical results.