Identification of source terms in the Schr\"odinger equation with dynamic boundary conditions from final data
Analysis of PDEs
2024-10-29 v1 Optimization and Control
Abstract
In this paper, we study an inverse problem of identifying two spatial-temporal source terms in the Schr\"odinger equation with dynamic 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 a gradient formula of the functional in terms of the solution to a suitable adjoint system, allowing us to obtain the Lipschitz continuity of the gradient. Next, the existence and uniqueness of a quasi-solution are also investigated. Finally, our theoretical results are validated by numerical experiments in one dimension using the Landweber iteration method.
Keywords
Cite
@article{arxiv.2410.21123,
title = {Identification of source terms in the Schr\"odinger equation with dynamic boundary conditions from final data},
author = {Salah-Eddine Chorfi and Alemdar Hasanov and Roberto Morales},
journal= {arXiv preprint arXiv:2410.21123},
year = {2024}
}