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arXiv · 2410.21123

Identification of source terms in the Schr\"odinger equation with dynamic boundary conditions from final data

Salah-Eddine Chorfi·Alemdar Hasanov·Roberto Morales
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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.

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Salah-Eddine Chorfi, Alemdar Hasanov, Roberto Morales. 2024-10-28. Identification of source terms in the Schr\"odinger equation with dynamic boundary conditions from final data. https://arxiv.org/abs/2410.21123

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