Determining A Sparse Space-Dependent Source Function In A Time-Fractional Diffusion-Wave Equation

In this thesis,we consider an inverse space-dependent source problem with a s-parse structure for a time-fractional diffusion-wave equation by the final time measure-ment data.Based on the expression to the solution of the direct problem,we transform the inverse space-dependent source problem into the first kind Fredholm integral equa-tion,then we discuss the uniqueness and ill-poseness of the inverse problem.We use the L1-L2 regularization method convert it into a nonsmooth variational problem,the semismooth Newton algorithm is developed to solve it.Numerical examples in one-dimensional and two-dimensional cases are provided to show the effectiveness and stability of the proposed method.