  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.
