No formulation of a new phase for a free boundary problem in combustion theory
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915269488672768 |
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| author | Furukawa, Ken Giga, Yoshikazu Kajiwara, Naoto |
| author_facet | Furukawa, Ken Giga, Yoshikazu Kajiwara, Naoto |
| contents | We consider a free boundary problem for the heat equation with a given non-negative external heat source. On the free boundary, we impose the zero Dirichlet condition and the fixed normal derivative so that heat escapes from the boundary. In various settings, we show that there exist no solutions when the initial temperature equals the fixed temperature no matter where the initial location of the free boundary is given provided that the external heat source is bounded from above. We also note that there is a chance to have a solution when the external temperature is unbounded as time tends to zero by giving a self-similar solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15662 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | No formulation of a new phase for a free boundary problem in combustion theory Furukawa, Ken Giga, Yoshikazu Kajiwara, Naoto Analysis of PDEs We consider a free boundary problem for the heat equation with a given non-negative external heat source. On the free boundary, we impose the zero Dirichlet condition and the fixed normal derivative so that heat escapes from the boundary. In various settings, we show that there exist no solutions when the initial temperature equals the fixed temperature no matter where the initial location of the free boundary is given provided that the external heat source is bounded from above. We also note that there is a chance to have a solution when the external temperature is unbounded as time tends to zero by giving a self-similar solution. |
| title | No formulation of a new phase for a free boundary problem in combustion theory |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2410.15662 |