Landweber iterative regularization method for an inverse initial value problem of diffusion equation with local and nonlocal operators

This paper considers an inverse initial value problem of diffusion equation with local and nonlocal operators. For this ill-posed problem, we give and prove a result of conditional stability. Meanwhile, Landweber iterative regularization method is used to overcome the ill-posedness, and based on the result of conditional stability, the convergence estimates of Holder type for regularization method are derived under the a-priori and a-posteriori choice rules for the regularized parameter. Finally, some numerical results are provided to show that Landweber iterative method works well in solving this inverse problem.