The fractional anisotropic Calderón problem for a nonlocal parabolic equation on closed Riemannian manifolds
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914985721987072 |
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| author | Lin, Yi-Hsuan |
| author_facet | Lin, Yi-Hsuan |
| contents | We consider the fractional anisotropic Calderón problem for the nonlocal parabolic equation $(\partial_t -Δ_g)^s u=f$ ($0<s<1$) on closed Riemannian manifolds. More concretely, we can determine the Riemannian manifold $(M,g)$ up to isometry by using the local source-to-solution map in an arbitrarily small open cylinder in the spacetime domain. This can be regarded as a nonlocal analog of the anisotropic Calderón problem in the parabolic setting. We also study several useful properties for nonlocal parabolic operators by using comprehensive spectrum analysis with semigroup theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17750 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The fractional anisotropic Calderón problem for a nonlocal parabolic equation on closed Riemannian manifolds Lin, Yi-Hsuan Analysis of PDEs Differential Geometry We consider the fractional anisotropic Calderón problem for the nonlocal parabolic equation $(\partial_t -Δ_g)^s u=f$ ($0<s<1$) on closed Riemannian manifolds. More concretely, we can determine the Riemannian manifold $(M,g)$ up to isometry by using the local source-to-solution map in an arbitrarily small open cylinder in the spacetime domain. This can be regarded as a nonlocal analog of the anisotropic Calderón problem in the parabolic setting. We also study several useful properties for nonlocal parabolic operators by using comprehensive spectrum analysis with semigroup theory. |
| title | The fractional anisotropic Calderón problem for a nonlocal parabolic equation on closed Riemannian manifolds |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2410.17750 |