The backward problem for an inhomogeneous time-fractional diffusion-wave equation in an axis-symmetric cylinder

In this paper, we consider the backward problem for an inhomogeneous time-fractional diffusion-wave equation in an axis-symmetric cylinder. This problem is ill-posed. In order to solve it stably, we give an iterative regularization method. The Holder error estimates are obtained under the a-priori and a-posteriori parameter choice rules. Numerical examples are presented to verify the effectiveness of our method.

Automated summary

In this paper, we address the ill-posed backward problem of an inhomogeneous time-fractional diffusion-wave equation in an axis-symmetric cylinder. To achieve stable solutions, we propose an iterative regularization method and derive Holder error estimates using a-priori and a-posteriori parameter choice rules. Numerical examples are provided to validate the effectiveness of our approach.