An inverse problem for the space-time fractional Schrödinger equation on closed manifolds
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917819280523264 |
|---|---|
| author | Li, Li |
| author_facet | Li, Li |
| contents | We formulate an inverse problem for an uncoupled space-time fractional Schrödinger equation on closed manifolds. Our main goal is to determine the fractional powers and the Riemannian metric (up to an isometry) simultaneously from the knowledge of the associated source-to-solution map. Our argument relies on the asymptotic behavior of Mittag-Leffler functions, Weyl's law for the eigenvalues of the Laplace-Beltrami operator, the unique continuation property of the space-fractional operator and the disjoint data metric determination result for the wave equation. We also provide a probabilistic formulation of our inverse problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20795 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An inverse problem for the space-time fractional Schrödinger equation on closed manifolds Li, Li Analysis of PDEs 35R11, 35R30 We formulate an inverse problem for an uncoupled space-time fractional Schrödinger equation on closed manifolds. Our main goal is to determine the fractional powers and the Riemannian metric (up to an isometry) simultaneously from the knowledge of the associated source-to-solution map. Our argument relies on the asymptotic behavior of Mittag-Leffler functions, Weyl's law for the eigenvalues of the Laplace-Beltrami operator, the unique continuation property of the space-fractional operator and the disjoint data metric determination result for the wave equation. We also provide a probabilistic formulation of our inverse problem. |
| title | An inverse problem for the space-time fractional Schrödinger equation on closed manifolds |
| topic | Analysis of PDEs 35R11, 35R30 |
| url | https://arxiv.org/abs/2410.20795 |