Inverse source problem for discrete Helmholtz equation
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914859786960896 |
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| author | Novikov, Roman Sharma, Basant Lal |
| author_facet | Novikov, Roman Sharma, Basant Lal |
| contents | We consider multi-frequency inverse source problem for the discrete Helmholtz operator on the square lattice $\mathbb{Z}^d$, $d \ge 1$. We consider this problem for the cases with and without phase information. We prove uniqueness results and present examples of non-uniqueness for this problem for the case of compactly supported source function, and a Lipshitz stability estimate for the phased case is established. Relations with inverse scattering problem for the discrete Schrödinger operators in the Born approximation are also provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14103 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inverse source problem for discrete Helmholtz equation Novikov, Roman Sharma, Basant Lal Analysis of PDEs Mathematical Physics We consider multi-frequency inverse source problem for the discrete Helmholtz operator on the square lattice $\mathbb{Z}^d$, $d \ge 1$. We consider this problem for the cases with and without phase information. We prove uniqueness results and present examples of non-uniqueness for this problem for the case of compactly supported source function, and a Lipshitz stability estimate for the phased case is established. Relations with inverse scattering problem for the discrete Schrödinger operators in the Born approximation are also provided. |
| title | Inverse source problem for discrete Helmholtz equation |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2401.14103 |