On a backward problem for nonlinear time fractional wave equations

In this paper, we concern with a backward problem for a nonlinear time fractional wave equation in a bounded domain. By applying the properties of Mittag-Leffler functions and the method of eigenvalue expansion, we establish some results about the existence and uniqueness of the mild solutions of the proposed problem based on the compact technique. Due to the ill-posedness of backward problem in the sense of Hadamard, a general filter regularization method is utilized to approximate the solution and further we prove the convergence rate for the regularized solutions.

Automated summary

This paper deals with a backward problem for a nonlinear time fractional wave equation in a bounded domain. By utilizing the properties of Mittag-Leffler functions and the method of eigenvalue expansion, we establish some results about the existence and uniqueness of mild solutions for the proposed problem based on compact technique. Due to the ill-posedness of the backward problem in the sense of Hadamard, a general filter regularization method is used to approximate the solution, and the convergence rate for the regularized solutions is proved.