Simultaneously reconstructing potentials and internal sources for fractional Schrödinger equations
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913517412548608 |
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| author | Li, Xinyan |
| author_facet | Li, Xinyan |
| contents | The inverse problems about fractional Calderón problem and fractional Schrödinger equations are of interest in the study of mathematics. In this paper, we propose the inverse problem to simultaneously reconstruct potentials and sources for fractional Schrödinger equations with internal source terms. We show the uniqueness for reconstructing the two terms under measurements from two different nonhomogeneous boundary conditions. By introducing the variational Tikhonov regularization functional, numerical method based on conjugate gradient method(CGM) is provided to realize this inverse problem. Numerical experiments are given to gauge the performance of the numerical method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16716 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Simultaneously reconstructing potentials and internal sources for fractional Schrödinger equations Li, Xinyan Numerical Analysis The inverse problems about fractional Calderón problem and fractional Schrödinger equations are of interest in the study of mathematics. In this paper, we propose the inverse problem to simultaneously reconstruct potentials and sources for fractional Schrödinger equations with internal source terms. We show the uniqueness for reconstructing the two terms under measurements from two different nonhomogeneous boundary conditions. By introducing the variational Tikhonov regularization functional, numerical method based on conjugate gradient method(CGM) is provided to realize this inverse problem. Numerical experiments are given to gauge the performance of the numerical method. |
| title | Simultaneously reconstructing potentials and internal sources for fractional Schrödinger equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2409.16716 |