Relationship among solutions for three-phase change problems with Robin, Dirichlet, and Neumann boundary conditions
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866917916887220224 |
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| author | Bollati, Julieta Natale, María Fernanda Semitiel, José Abel Tarzia, Domingo Alberto |
| author_facet | Bollati, Julieta Natale, María Fernanda Semitiel, José Abel Tarzia, Domingo Alberto |
| contents | This study investigates the melting process of a three-phase Stefan problem in a semi-infinite material, imposing a convective boundary condition at the fixed face. By employing a similarity-type transformation, the problem is reduced to a solvable form, yielding a unique explicit solution. The analysis uncovers significant equivalences among the solutions of three different three-phase Stefan problems: one with a Robin boundary condition, another with a Dirichlet boundary condition, and a third one with a Neumann boundary condition at the fixed face. These equivalences are established under the condition that the problem data satisfy a specific relationship, providing new insights into the behaviour of phase change problems under varying boundary conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05545 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Relationship among solutions for three-phase change problems with Robin, Dirichlet, and Neumann boundary conditions Bollati, Julieta Natale, María Fernanda Semitiel, José Abel Tarzia, Domingo Alberto Analysis of PDEs This study investigates the melting process of a three-phase Stefan problem in a semi-infinite material, imposing a convective boundary condition at the fixed face. By employing a similarity-type transformation, the problem is reduced to a solvable form, yielding a unique explicit solution. The analysis uncovers significant equivalences among the solutions of three different three-phase Stefan problems: one with a Robin boundary condition, another with a Dirichlet boundary condition, and a third one with a Neumann boundary condition at the fixed face. These equivalences are established under the condition that the problem data satisfy a specific relationship, providing new insights into the behaviour of phase change problems under varying boundary conditions. |
| title | Relationship among solutions for three-phase change problems with Robin, Dirichlet, and Neumann boundary conditions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2502.05545 |