关于双非局域 Hele-Shaw-Cahn-Hilliard 系统：推导与二维拟合

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Nonlinear Science Pub Date : 2024-03-15 DOI:10.1007/s00332-024-10018-6

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引用次数: 0

摘要

摘要从经典的非局部（空间）Cahn-Hilliard-Stokes 模型开始，我们通过数学同质化严格推导出了一个新的有效混合模型，该模型由一个非局部（时间）Hele-Shaw 方程和一个非局部（空间）Cahn-Hilliard 方程耦合而成。然后，我们对由此产生的模型进行分析，并证明其良好拟合性。分析的关键是薄异质域中的西格玛收敛新概念，它允许同时通过异质和域厚度的均质化极限。

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

Abstract

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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来源期刊

Journal of Nonlinear Science 数学-力学

CiteScore

5.00

自引率

3.30%

发文量

审稿时长

4.5 months

期刊介绍： The mission of the Journal of Nonlinear Science is to publish papers that augment the fundamental ways we describe, model, and predict nonlinear phenomena. Papers should make an original contribution to at least one technical area and should in addition illuminate issues beyond that area''s boundaries. Even excellent papers in a narrow field of interest are not appropriate for the journal. Papers can be oriented toward theory, experimentation, algorithms, numerical simulations, or applications as long as the work is creative and sound. Excessively theoretical work in which the application to natural phenomena is not apparent (at least through similar techniques) or in which the development of fundamental methodologies is not present is probably not appropriate. In turn, papers oriented toward experimentation, numerical simulations, or applications must not simply report results without an indication of what a theoretical explanation might be. All papers should be submitted in English and must meet common standards of usage and grammar. In addition, because ours is a multidisciplinary subject, at minimum the introduction to the paper should be readable to a broad range of scientists and not only to specialists in the subject area. The scientific importance of the paper and its conclusions should be made clear in the introduction-this means that not only should the problem you study be presented, but its historical background, its relevance to science and technology, the specific phenomena it can be used to describe or investigate, and the outstanding open issues related to it should be explained. Failure to achieve this could disqualify the paper.