On a local solvability of the contact Muskat problem
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910708843675648 |
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| author | Vasylyeva, Nataliya |
| author_facet | Vasylyeva, Nataliya |
| contents | In the paper, we discuss the two-dimensional contact Muskat problem with zero surface tension of a free boundary. The initial shape of the unknown interface is a smooth simple curve which forms acute corners $δ_{0}$ and $δ_{1}$ with fixed boundaries. Under suitable assumptions on the given data, the one-to-one local classical solvability of this problem is proved. We also describe the sufficient conditions on the data in the model which provide the existence of the "waiting time" phenomenon. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14859 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a local solvability of the contact Muskat problem Vasylyeva, Nataliya Analysis of PDEs In the paper, we discuss the two-dimensional contact Muskat problem with zero surface tension of a free boundary. The initial shape of the unknown interface is a smooth simple curve which forms acute corners $δ_{0}$ and $δ_{1}$ with fixed boundaries. Under suitable assumptions on the given data, the one-to-one local classical solvability of this problem is proved. We also describe the sufficient conditions on the data in the model which provide the existence of the "waiting time" phenomenon. |
| title | On a local solvability of the contact Muskat problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2411.14859 |