Reconstruction of the initial condition in parabolic equations with Log-Lipschitz coefficients
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929396305100800 |
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| author | Del Santo, Daniele Prizzi, Martino |
| author_facet | Del Santo, Daniele Prizzi, Martino |
| contents | We consider a parabolic equation whose coefficients are Log-Lipschitz continuous in $t$ and Lipschitz continuous in $x$. Combining a recent conditional stability result with a well posed variational problem, we reconstruct the initial condition of an unknown solution from a rough measurement at the final time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03837 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reconstruction of the initial condition in parabolic equations with Log-Lipschitz coefficients Del Santo, Daniele Prizzi, Martino Analysis of PDEs 35B30, 35K10, 35R25 We consider a parabolic equation whose coefficients are Log-Lipschitz continuous in $t$ and Lipschitz continuous in $x$. Combining a recent conditional stability result with a well posed variational problem, we reconstruct the initial condition of an unknown solution from a rough measurement at the final time. |
| title | Reconstruction of the initial condition in parabolic equations with Log-Lipschitz coefficients |
| topic | Analysis of PDEs 35B30, 35K10, 35R25 |
| url | https://arxiv.org/abs/2401.03837 |