Identification of the zeroth-order coefficient and fractional order in a time-fractional reaction-diffusion-wave equation

In this paper, we investigate an inverse problem of recovering the zeroth-order coefficient and fractional order simultaneously in a time-fractional reaction-diffusion-wave equation by using boundary measurement data from both of uniqueness and numerical method. We prove the uniqueness of the considered inverse problem and the Lipschitz continuity of the forward operator. Then the inverse problem is formulated into a variational problem by the Tikhonov-type regularization. Based on the continuity of the forward operator, we prove that the minimizer of the Tikhonov-type functional exists and converges to the exact solution under an a priori choice of regularization parameter. The steepest descent method combined with Nesterov acceleration is adopted to solve the variational problem. Three numerical examples are presented to support the efficiency and rationality of our proposed method.

Automated summary

This paper investigates an inverse problem of recovering the zeroth-order coefficient and fractional order simultaneously in a time-fractional reaction-diffusion-wave equation using boundary measurement data. The uniqueness of the considered inverse problem and the Lipschitz continuity of the forward operator are proven. The inverse problem is formulated into a variational problem with Tikhonov-type regularization, and the existence of the minimizer is proved under an a priori choice of regularization parameter. The proposed method is solved using the steepest descent method combined with Nesterov acceleration, and its efficiency and rationality are supported by numerical examples.