Exact solution structures on some nonlocal overdetermined problems
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918251796103168 |
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| author | Sato, Kazuki Takahashi, Futoshi |
| author_facet | Sato, Kazuki Takahashi, Futoshi |
| contents | In this paper, we study the solution structures of Serrin-type overdetermined problems with Kirchhoff-type nonlocal terms. We prove that the exact number of solutions is the same as those of some transcendental equations defined by the nonlocal terms. We also obtain the explicit form of solutions by using the unique solutions of the overdetermined problems without the nonlocal terms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14987 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact solution structures on some nonlocal overdetermined problems Sato, Kazuki Takahashi, Futoshi Analysis of PDEs 34C23, 37G99 In this paper, we study the solution structures of Serrin-type overdetermined problems with Kirchhoff-type nonlocal terms. We prove that the exact number of solutions is the same as those of some transcendental equations defined by the nonlocal terms. We also obtain the explicit form of solutions by using the unique solutions of the overdetermined problems without the nonlocal terms. |
| title | Exact solution structures on some nonlocal overdetermined problems |
| topic | Analysis of PDEs 34C23, 37G99 |
| url | https://arxiv.org/abs/2512.14987 |