Inverse problems for first-order hyperbolic equations with time-dependent coefficients
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866909535835258880 |
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| author | Floridia, Giuseppe Takase, Hiroshi |
| author_facet | Floridia, Giuseppe Takase, Hiroshi |
| contents | We prove global Lipschitz stability for inverse source and coefficient problems for first-order linear hyperbolic equations, the coefficients of which depend on both space and time. We use a global Carleman estimate, and a crucial point, introduced in this paper, is the choice of the length of integral curves of a vector field generated by the principal part of the hyperbolic operator to construct a weight function for the Carleman estimate. These integral curves correspond to the characteristic curves in some cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_12039 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Inverse problems for first-order hyperbolic equations with time-dependent coefficients Floridia, Giuseppe Takase, Hiroshi Analysis of PDEs We prove global Lipschitz stability for inverse source and coefficient problems for first-order linear hyperbolic equations, the coefficients of which depend on both space and time. We use a global Carleman estimate, and a crucial point, introduced in this paper, is the choice of the length of integral curves of a vector field generated by the principal part of the hyperbolic operator to construct a weight function for the Carleman estimate. These integral curves correspond to the characteristic curves in some cases. |
| title | Inverse problems for first-order hyperbolic equations with time-dependent coefficients |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2009.12039 |