Zeitschrift fur Angewandte Mathematik und Physik, cilt.76, sa.3, 2025 (SCI-Expanded, Scopus)
In this paper, we study an inverse problem of retrieving two spatial–temporal source terms in the Schrödinger equation with dynamical boundary conditions from the final time overdetermination. We adopt a weak solution approach to solve the inverse source problem. By analyzing the associated Tikhonov functional, we prove an explicit formula for the functional gradient via the solution to a suitable adjoint backward system, allowing us to obtain the Lipschitz continuity of the gradient. Then, the existence and uniqueness of a quasi-solution are also investigated. Finally, our theoretical results are illustrated by numerical experiments in one dimension using the Landweber iteration method.