The evolving surface Cahn-Hilliard equation with a degenerate mobility
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911087313551360 |
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| author | Elliott, Charles M. Sales, Thomas |
| author_facet | Elliott, Charles M. Sales, Thomas |
| contents | We consider the existence of suitable weak solutions to the Cahn-Hilliard equation with a non-constant (degenerate) mobility on a class of evolving surfaces. We also show weak-strong uniqueness for the case of a positive mobility function, and under some further assumptions on the initial data we show uniqueness for a class of strong solutions for a degenerate mobility function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_24147 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The evolving surface Cahn-Hilliard equation with a degenerate mobility Elliott, Charles M. Sales, Thomas Analysis of PDEs 35K65 (Primary), 35K55, 35Q79 (Secondary) We consider the existence of suitable weak solutions to the Cahn-Hilliard equation with a non-constant (degenerate) mobility on a class of evolving surfaces. We also show weak-strong uniqueness for the case of a positive mobility function, and under some further assumptions on the initial data we show uniqueness for a class of strong solutions for a degenerate mobility function. |
| title | The evolving surface Cahn-Hilliard equation with a degenerate mobility |
| topic | Analysis of PDEs 35K65 (Primary), 35K55, 35Q79 (Secondary) |
| url | https://arxiv.org/abs/2410.24147 |