A one-dimensional Stefan problem for the heat equation with a nonlinear boundary condition
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911240372092928 |
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| author | Araya, Kensho Ishige, Kazuhiro |
| author_facet | Araya, Kensho Ishige, Kazuhiro |
| contents | We study the one-dimensional one-phase Stefan problem for the heat equation with a nonlinear boundary condition. We show that all solutions fall into one of three distinct types: global-in-time solutions with exponential decay, global-in-time solutions with non-exponential decay, and finite-time blow-up solutions. The classification depends on the size of the initial function. Furthermore, we describe the behavior of solutions at the blow-up time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26088 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A one-dimensional Stefan problem for the heat equation with a nonlinear boundary condition Araya, Kensho Ishige, Kazuhiro Analysis of PDEs We study the one-dimensional one-phase Stefan problem for the heat equation with a nonlinear boundary condition. We show that all solutions fall into one of three distinct types: global-in-time solutions with exponential decay, global-in-time solutions with non-exponential decay, and finite-time blow-up solutions. The classification depends on the size of the initial function. Furthermore, we describe the behavior of solutions at the blow-up time. |
| title | A one-dimensional Stefan problem for the heat equation with a nonlinear boundary condition |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.26088 |