Stability estimates of inverse random source problems for the wave equations by using correlation-based data
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913540219076608 |
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| author | Li, Peijun Liang, Ying Wang, Xu |
| author_facet | Li, Peijun Liang, Ying Wang, Xu |
| contents | This paper focuses on stability estimates of the inverse random source problems for the polyharmonic, electromagnetic, and elastic wave equations. The source is represented as a microlocally isotropic Gaussian random field, which is defined by its covariance operator in the form of a classical pseudo-differential operator. The inverse problem is to determine the strength function of the principal symbol by exploiting the correlation of far-field patterns associated with the stochastic wave equations at a single frequency. For the first time, we show in a unified framework that the optimal Lipschitz-type stability can be attained across all the considered wave equations through the utilization of correlation-based data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07938 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability estimates of inverse random source problems for the wave equations by using correlation-based data Li, Peijun Liang, Ying Wang, Xu Analysis of PDEs 35R30, 35R60 This paper focuses on stability estimates of the inverse random source problems for the polyharmonic, electromagnetic, and elastic wave equations. The source is represented as a microlocally isotropic Gaussian random field, which is defined by its covariance operator in the form of a classical pseudo-differential operator. The inverse problem is to determine the strength function of the principal symbol by exploiting the correlation of far-field patterns associated with the stochastic wave equations at a single frequency. For the first time, we show in a unified framework that the optimal Lipschitz-type stability can be attained across all the considered wave equations through the utilization of correlation-based data. |
| title | Stability estimates of inverse random source problems for the wave equations by using correlation-based data |
| topic | Analysis of PDEs 35R30, 35R60 |
| url | https://arxiv.org/abs/2410.07938 |