Derivation and analysis of a nonlocal Hele-Shaw-Cahn-Hilliard system for flow in thin heterogeneous layers
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914739208060928 |
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| author | Cardone, Giuseppe Jäger, Willi Woukeng, Jean Louis |
| author_facet | Cardone, Giuseppe Jäger, Willi Woukeng, Jean Louis |
| contents | We derive, through the deterministic homogenization theory in thin domains, a new model consisting of Hele-Shaw equation with memory coupled with the convective Cahn-Hilliard equation. The obtained system, which models in particular tumor growth, is then analyzed and we prove its well-posedness in dimension 2. To achieve our goal, we develop and use the new concept of sigma-convergence in thin heterogeneous media, and we prove some regularity results for the upscaled model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02306 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Derivation and analysis of a nonlocal Hele-Shaw-Cahn-Hilliard system for flow in thin heterogeneous layers Cardone, Giuseppe Jäger, Willi Woukeng, Jean Louis Analysis of PDEs 35B40, 35K65, 46J10 We derive, through the deterministic homogenization theory in thin domains, a new model consisting of Hele-Shaw equation with memory coupled with the convective Cahn-Hilliard equation. The obtained system, which models in particular tumor growth, is then analyzed and we prove its well-posedness in dimension 2. To achieve our goal, we develop and use the new concept of sigma-convergence in thin heterogeneous media, and we prove some regularity results for the upscaled model. |
| title | Derivation and analysis of a nonlocal Hele-Shaw-Cahn-Hilliard system for flow in thin heterogeneous layers |
| topic | Analysis of PDEs 35B40, 35K65, 46J10 |
| url | https://arxiv.org/abs/2404.02306 |