Simultaneous inversion of two initial values for a time-fractional diffusion-wave equation

This study is devoted to recovering two initial values for a time-fractional diffusion-wave equation from boundary Cauchy data. We provide the uniqueness result for recovering two initial values simultaneously by the method of Laplace transformation and analytic continuation. And then we use a nonstationary iterative Tikhonov regularization method to solve the inverse problem and propose a finite dimensional approximation algorithm to find good approximations to the initial values. Numerical examples in one- and two-dimensional cases are provided to show the effectiveness of the proposed method.

Automated summary

This study introduces a method to recover two initial values for a time-fractional diffusion-wave equation, achieving uniqueness by Laplace transformation and analytic continuation, followed by solving the inverse problem using an iterative Tikhonov regularization method and proposing a finite dimensional approximation algorithm for finding good approximations to the initial values. Numerical examples in one- and two-dimensional cases demonstrate the effectiveness of the proposed method.