Identification of source terms in the Schrödinger equation with dynamic boundary conditions from final data

2024/10/28 by S. E. Chorfi, Chorfi, Salah-Eddine, Alemdar Hasanov +3 · 2 citations
Mathematics · Engineering · #Numerical methods in inverse problems #Terahertz technology and applications #Electromagnetic Simulation and Numerical Methods

paper · pdf · doi:10.48550/arxiv.2410.21123

Abstract

In this paper, we study an inverse problem of identifying two spatial-temporal source terms in the Schrödinger 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.

Cited by

• Identification of Source Terms in the Ginzburg-Landau Equation from Final Data
• Forward and backward problems for abstract time-fractional Schrödinger equations

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