Stability for inverse random source problems of the polyharmonic wave equation
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910648685821952 |
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| author | Li, Peijun Li, Zhenqian Liang, Ying |
| author_facet | Li, Peijun Li, Zhenqian Liang, Ying |
| contents | This paper investigates stability estimates for inverse source problems in the stochastic polyharmonic wave equation, where the source is represented by white noise. The study examines the well-posedness of the direct problem and derives stability estimates for identifying the strength of the random source. Assuming a priori information of the regularity and support of the source strength, the Hölder stability is established in the absence of a potential. In the more challenging case where a potential is present, the logarithmic stability estimate is obtained by constructing specialized solutions to the polyharmonic wave equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10016 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability for inverse random source problems of the polyharmonic wave equation Li, Peijun Li, Zhenqian Liang, Ying Analysis of PDEs Mathematical Physics 35R30, 35R60 This paper investigates stability estimates for inverse source problems in the stochastic polyharmonic wave equation, where the source is represented by white noise. The study examines the well-posedness of the direct problem and derives stability estimates for identifying the strength of the random source. Assuming a priori information of the regularity and support of the source strength, the Hölder stability is established in the absence of a potential. In the more challenging case where a potential is present, the logarithmic stability estimate is obtained by constructing specialized solutions to the polyharmonic wave equation. |
| title | Stability for inverse random source problems of the polyharmonic wave equation |
| topic | Analysis of PDEs Mathematical Physics 35R30, 35R60 |
| url | https://arxiv.org/abs/2410.10016 |