Derivation and analysis of a nonlocal Hele-Shaw-Cahn-Hilliard system for flow in thin heterogeneous layers
arXiv:2404.02306 · doi:10.1142/S0218202524500246
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.
52 pages