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arXiv · 2404.02306

Derivation and analysis of a nonlocal Hele-Shaw-Cahn-Hilliard system for flow in thin heterogeneous layers

Giuseppe Cardone·Willi Jäger·Jean Louis Woukeng
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Abstract

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.

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Giuseppe Cardone, Willi Jäger, Jean Louis Woukeng. 2024-04-02. Derivation and analysis of a nonlocal Hele-Shaw-Cahn-Hilliard system for flow in thin heterogeneous layers. https://doi.org/10.1142/s0218202524500246

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