A Quasi-reversibility Method To Identify A Space-dependent Source For A Time-fractional Diffusion-wave Equation

In this paper,we study a problem of recovering a space-dependent source term for a time-fractional diffusion-wave equation in a bounded domain,that is,we use the final time noisy data to recover the space-dependent source.Firstly,based on the series expression of the solution about the direct problem,the inverse problem is transformed into the first kind of integral equation,we discuss the uniqueness,ill-posedness and conditional stability of the inverse problem.Then we propose a quasi-reversibility regularization method to transform the inverse problem into a regularied problem,and prove the well-posedness of the regularied problem,and give two convergence order estimations by using an a priori and an a posteriori choice rule for the regularization parameter respectively.Finally,numerical examples are presented which demonstrate the effectiveness of the regularization methods and confirm the theoretical results.