Existence of Weak Solutions to a Cahn-Hilliard-Biot System
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| Format: | Preprint |
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2024
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| _version_ | 1866910576029990912 |
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| author | Abels, Helmut Garcke, Harald Haselböck, Jonas |
| author_facet | Abels, Helmut Garcke, Harald Haselböck, Jonas |
| contents | We prove existence of weak solutions to 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, and is further augmented by a visco-elastic regularization of Kelvin-Voigt type. To obtain this result, we approximate the problem in two steps, where first a semi-Galerkin ansatz is employed to show existence of weak solutions to regularized systems, for which later on compactness arguments allow limit passage. Notably, we also establish a maximal regularity theory for linear visco-elastic problems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_07515 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of Weak Solutions to a Cahn-Hilliard-Biot System Abels, Helmut Garcke, Harald Haselböck, Jonas Analysis of PDEs 35A01, 35D30, 35K41, 74B10 We prove existence of weak solutions to 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, and is further augmented by a visco-elastic regularization of Kelvin-Voigt type. To obtain this result, we approximate the problem in two steps, where first a semi-Galerkin ansatz is employed to show existence of weak solutions to regularized systems, for which later on compactness arguments allow limit passage. Notably, we also establish a maximal regularity theory for linear visco-elastic problems. |
| title | Existence of Weak Solutions to a Cahn-Hilliard-Biot System |
| topic | Analysis of PDEs 35A01, 35D30, 35K41, 74B10 |
| url | https://arxiv.org/abs/2403.07515 |