The Existence And Regularity Of Solutions For Backward Problems Of Time Fractional Diffusion Equations

We mainly study the existence and regularity of the solution for backward problems of the time fractional diffusion equation,which can be used to describe some abnormal diffusion phenomena.Therefore,the research on the equation has attracted people's close attention.In Chapter 2,we study the existence of solutions for backward problems of time fractional coupled diffusion systems.Firstly,we establish the definition of mild solutions and further discuss the related properties of solution operators.Then,we obtain the existence results of solution by using the Banach fixed point theorem and the Krasnoselskii fixed point theorem respectively.In Chapter 3,we study the regularity of solutions for backward problems of time fractional diffusion equations.Firstly,the regularity of solutions of linear problems is obtained by using the properties of Mittag-Leffler functions.Then,the ill-posedness of the problem in the homogeneous case is analyzed,and the regularized solution of the problem is obtained by fractional Tikhonov regularization method.Finally,the convergence analysis of the regular solution and the mild solution is given under an a prior and an a posterior regularization parameter choice rules.