Local Well-Posedness of the Cahn-Hilliard-Biot System
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914517349302272 |
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| author | Abels, Helmut Haselböck, Jonas |
| author_facet | Abels, Helmut Haselböck, Jonas |
| contents | We show short-time well-posedness of a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly couples Biot's equations for poroelasticity, including phase-field dependent material properties, with the Cahn-Hilliard equation to model the evolution of the solid, where we further distinguish between the absence and presence of a visco-elastic term of Kelvin-Voigt type. While both problems will be reduced to a fixed-point equation that can be solved using maximal regularity theory along with a contraction argument, the first case relies on a semigroup approach over suitable Hilbert spaces, whereas treating the second case under minimal assumptions with respect to spatial regularity necessitates the application of Banach scales. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17893 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local Well-Posedness of the Cahn-Hilliard-Biot System Abels, Helmut Haselböck, Jonas Analysis of PDEs 35A01, 35A02, 35K41, 74B10, 76S05 We show short-time well-posedness of a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly couples Biot's equations for poroelasticity, including phase-field dependent material properties, with the Cahn-Hilliard equation to model the evolution of the solid, where we further distinguish between the absence and presence of a visco-elastic term of Kelvin-Voigt type. While both problems will be reduced to a fixed-point equation that can be solved using maximal regularity theory along with a contraction argument, the first case relies on a semigroup approach over suitable Hilbert spaces, whereas treating the second case under minimal assumptions with respect to spatial regularity necessitates the application of Banach scales. |
| title | Local Well-Posedness of the Cahn-Hilliard-Biot System |
| topic | Analysis of PDEs 35A01, 35A02, 35K41, 74B10, 76S05 |
| url | https://arxiv.org/abs/2508.17893 |