On the regularization of solution of an inverse ultraparabolic equation associated with perturbed final data

In this paper, we study the inverse problem for a class of abstract ultraparabolic equations which is well-known to be ill-posed. We employ some elementary results of semi-group theory to present the formula of solution, then show the instability cause. Since the solution exhibits unstable dependence on the given data functions, we propose a new regularization method to stabilize the solution. then obtain the error estimate. A numerical example shows that the method is efficient and feasible. This work slightly extends to the earlier results in Zouyed et al. \cite{key-9} (2014).