On the Doubly Non-local Hele-Shaw-Cahn-Hilliard System: Derivation and 2D Well-Posedness

被引：0
作者：
Peter, Malte A. [1 ,2 ]
Woukeng, Jean Louis [1 ,3 ]
机构：
[1] Univ Augsburg, Inst Math, Univ Str 12a, D-86159 Augsburg, Germany
[2] Univ Augsburg, Ctr Adv Analyt & Predict Sci, Univ Str 12a, D-86159 Augsburg, Germany
[3] Univ Dschang, Dept Math & Comp Sci, POB 67, Dschang, Cameroon
来源：
JOURNAL OF NONLINEAR SCIENCE | 2024年 / 34卷 / 03期
关键词：
Non-local Cahn-Hilliard-Stokes system; Sigma-convergence; Thin domains; Doubly non-local Hele-Shaw-Cahn-Hilliard system; Homogenization; EFFECTIVE TRANSMISSION CONDITIONS; DIFFUSE INTERFACE MODEL; NAVIER-STOKES SYSTEMS; LONG-TIME BEHAVIOR; POROUS-MEDIA; HOMOGENIZATION; EQUATIONS; DOMAINS; CONVERGENCE; SIMULATION;
D O I：
10.1007/s00332-024-10018-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Starting from a classic non-local (in space) Cahn-Hilliard-Stokes model for two-phase flow in a thin heterogeneous fluid domain, we rigorously derive by mathematical homogenization a new effective mixture model consisting of a coupling of a non-local (in time) Hele-Shaw equation with a non-local (in space) Cahn-Hilliard equation. We then analyse the resulting model and prove its well-posedness. A key to the analysis is the new concept of sigma-convergence in thin heterogeneous domains allowing to pass to the homogenization limit with respect to the heterogeneities and the domain thickness simultaneously.
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页数：56
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