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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.18641 |
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| _version_ | 1866917030520684544 |
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| author | Lai, Ru-Yu Lin, Yi-Hsuan Yan, Lili |
| author_facet | Lai, Ru-Yu Lin, Yi-Hsuan Yan, Lili |
| contents | We examine inverse problems for the variable-coefficient nonlocal parabolic operator $(\partial_t - Δ_g)^s$, where $0 < s < 1$. This article makes two primary contributions. First, we introduce a novel entanglement principle for these operators under suitable smoothness conditions. Second, we prove that lower-order perturbations can be uniquely determined from the associated Dirichlet-to-Neumann map using this principle. However, due to insufficient solution regularity, direct application of the entanglement principle to the inverse problem is not feasible. To address this, we derive a modified entanglement principle, enabling the effective resolution of related inverse problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_18641 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Entanglement principle and fractional Calderón problem for nonlocal parabolic operators Lai, Ru-Yu Lin, Yi-Hsuan Yan, Lili Analysis of PDEs We examine inverse problems for the variable-coefficient nonlocal parabolic operator $(\partial_t - Δ_g)^s$, where $0 < s < 1$. This article makes two primary contributions. First, we introduce a novel entanglement principle for these operators under suitable smoothness conditions. Second, we prove that lower-order perturbations can be uniquely determined from the associated Dirichlet-to-Neumann map using this principle. However, due to insufficient solution regularity, direct application of the entanglement principle to the inverse problem is not feasible. To address this, we derive a modified entanglement principle, enabling the effective resolution of related inverse problems. |
| title | Entanglement principle and fractional Calderón problem for nonlocal parabolic operators |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.18641 |