Identification of source terms in the Schrödinger equation with dynamic boundary conditions from final data
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929563382054912 |
|---|---|
| author | Chorfi, Salah-Eddine Hasanov, Alemdar Morales, Roberto |
| author_facet | Chorfi, Salah-Eddine Hasanov, Alemdar Morales, Roberto |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_21123 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Identification of source terms in the Schrödinger equation with dynamic boundary conditions from final data Chorfi, Salah-Eddine Hasanov, Alemdar Morales, Roberto Analysis of PDEs Optimization and Control 35J10, 35R25, 35R30, 49N45, 47A05 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. |
| title | Identification of source terms in the Schrödinger equation with dynamic boundary conditions from final data |
| topic | Analysis of PDEs Optimization and Control 35J10, 35R25, 35R30, 49N45, 47A05 |
| url | https://arxiv.org/abs/2410.21123 |