Partial data inverse problems for the nonlinear magnetic Schrödinger equation
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929586354257920 |
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| author | Lai, Ru-Yu Uhlmann, Gunther Yan, Lili |
| author_facet | Lai, Ru-Yu Uhlmann, Gunther Yan, Lili |
| contents | In this paper, we study the partial data inverse problem for nonlinear magnetic Schrödinger equations. We show that the knowledge of the Dirichlet-to-Neumann map, measured on an arbitrary part of the boundary, determines the time-dependent linear coefficients, electric and magnetic potentials, and nonlinear coefficients, provided that the divergence of the magnetic potential is given. Additionally, we also investigate both the forward and inverse problems for the linear magnetic Schrödinger equation with a time-dependent leading term. In particular, all coefficients are uniquely recovered from boundary data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06369 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Partial data inverse problems for the nonlinear magnetic Schrödinger equation Lai, Ru-Yu Uhlmann, Gunther Yan, Lili Analysis of PDEs In this paper, we study the partial data inverse problem for nonlinear magnetic Schrödinger equations. We show that the knowledge of the Dirichlet-to-Neumann map, measured on an arbitrary part of the boundary, determines the time-dependent linear coefficients, electric and magnetic potentials, and nonlinear coefficients, provided that the divergence of the magnetic potential is given. Additionally, we also investigate both the forward and inverse problems for the linear magnetic Schrödinger equation with a time-dependent leading term. In particular, all coefficients are uniquely recovered from boundary data. |
| title | Partial data inverse problems for the nonlinear magnetic Schrödinger equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2411.06369 |