The Existence Of Solutions For Initial Value Problem And Terminal Problem Of A Class Of Fractional Pseudo-parabolic Equations

Fractional pseudo-parabolic equations are a type of nonclassical diffusion equations.Compared with the classical diffusion equations,they are usually used to describe accurately materials and processes with historical memory and genetic properties.Therefore,fractional pseudo-parabolic equations have a wide range of applications in natural sciences and engineering technology.This paper mainly studies the initial value problem and the terminal value problem of a class of fractional pseudo-parabolic equations,respectively.In Chapter 2,when the nonlinear source term satisfies the Lipschitz condition,we study the existence and uniqueness of mild solutions of the initial value problem for the fractional pseudo-parabolic equations by using the Banach contraction mapping principle.Then when the nonlinear source term satisfies the linear growth condition,we use the Schauder fixed point theorem to obtain the existence result of mild solutions of the initial value problem.In Chapter 3,if 0 <?< 1,we use the relevant properties of the Hausdorff measure of noncompactness and the Darbo-Sadovskii fixed point theorem to prove the existence result of mild solutions of the terminal value problem for the fractional pseudo-parabolic equations.If 1 <?< 2,the terminal value problem is ill-posed in the meaning of Hadamard,then we use the fractional order Landweber regularization method to get the regularized solution of the terminal value problem,and give the error estimate between the mild solution and the regularized solution using a prior choice rules.