An Inverse Initial Value Problem For A Time Fractional Diffusion Wave Equation

In this thesis,we consider an inverse initial value problem for a time fractional diffusion wave equation.That is to determine an initial data from a noisy final data.Due to the ill-posedness of the inverse initial value problem,we apply the Tikhonov regularization method to transform the inverse problem into a variational problem.And take the minimizier as the regularizied solution of the inverse problem.The estimates of convergence rates are given by using an a priori regularization parameter choice rule and an a posteriori regularization parameter choice rule.Numerical examples show the effctiveness of the proposed method.