Backward Problem For Time Fractional Diffusion Equation On Spherically Symmetric Ddomain

The backward problem is a very important type of inverse problem.It is widely used in engineering and other fields.Consequently,the study of the backward problem of fractional diffusion equation plays an important role in the development of many fields.This paper mainly discusses the backward problem of the time fractional diffusion equation on spherically symmetric domain.In chapter 2,by introducing a weighted H(?)lder continuous function,and using the properties of Mittag-Leffer function,Wright function and the method of eigenvalue expansion,we give some results about the existence,uniqueness,and regularity of the mild solution to the backward problem of linear time fractional diffusion equations.Secondly,the existence and uniqueness results of the mild solution in nonlinear situation are established by using the Banach contraction mapping principle.The conclusions given here generalize some existing results;In chapter 3,since the backward problem of the linear time fractional diffusion equation backward problems is ill-posed,we use a fractional Tikhonov regularization method to establish the regularization solution of the problem,and the convergence estimates under the two regularization parameter selection rules are also given.