Two parabolic inverse problems for an equation with unbounded zero-order coefficient
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917867812814848 |
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| author | Choulli, Mourad |
| author_facet | Choulli, Mourad |
| contents | This work is composed of two parts. We prove in the first part the uniqueness of the determination of the unbounded zero-order coefficient in a parabolic equation from boundary measurements. The novelty of our result is that it covers the largest class of unbounded zero-order coefficients. We establish in the second part a logarithmic stability inequality for the problem of determining the initial condition from a single interior measurement. As by-product, we obtain an observability inequality for a parabolic equation with unbounded zero-order coefficient. The proof of this observability inequality is based on a new global quantitative unique continuation for the Schrödinger equation with unbounded potential. For the sake of completeness, we provide in Appendix A a full proof of this result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02901 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two parabolic inverse problems for an equation with unbounded zero-order coefficient Choulli, Mourad Analysis of PDEs 35R30 This work is composed of two parts. We prove in the first part the uniqueness of the determination of the unbounded zero-order coefficient in a parabolic equation from boundary measurements. The novelty of our result is that it covers the largest class of unbounded zero-order coefficients. We establish in the second part a logarithmic stability inequality for the problem of determining the initial condition from a single interior measurement. As by-product, we obtain an observability inequality for a parabolic equation with unbounded zero-order coefficient. The proof of this observability inequality is based on a new global quantitative unique continuation for the Schrödinger equation with unbounded potential. For the sake of completeness, we provide in Appendix A a full proof of this result. |
| title | Two parabolic inverse problems for an equation with unbounded zero-order coefficient |
| topic | Analysis of PDEs 35R30 |
| url | https://arxiv.org/abs/2411.02901 |