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

• Verfasst von: Cardone, Giuseppe [VerfasserIn]
• Verfasst von: Jäger, Willi [VerfasserIn]
• Verfasst von: Woukeng, Jean Louis [VerfasserIn]
• Titel: Derivation and analysis of a nonlocal Hele-Shaw-Cahn-Hilliard system for flow in thin heterogeneous layers
• Verf.angabe: Giuseppe Cardone, Willi Jäger, Jean Louis Woukeng
• E-Jahr: 2024
• Jahr: Juni 2024
• Umfang: 57 S.
• Fussnoten: Online veröffentlicht: 8. März 2024 ; Gesehen am 30.07.2024
• Titel Quelle: Enthalten in: Mathematical models and methods in applied sciences (M 3 AS)
• Ort Quelle: Singapore [u.a.] : World Scientific, 1991
• Jahr Quelle: 2024
• Band/Heft Quelle: 34(2024), 7 vom: Juni, Seite 1343-1400
• ISSN Quelle: 1793-6314
• DOI: doi:10.1142/S0218202524500246
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: algebras with mean value
• Sach-SW: homogenization
• Sach-SW: sigma-convergence
• Sach-SW: Thin heterogeneous domains
• K10plus-PPN: 1896922910

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.