具有趋化性和一般源项的分层肿瘤生长多相Cahn-Hilliard-Darcy和Cahn-Hilliard-Brinkman模型弱解的存在性

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
P. Knopf, A. Signori
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引用次数: 12

摘要

摘要我们研究了一个具有一般源项的肿瘤生长的多阶段Cahn–Hilliard模型。多阶段方法使我们能够考虑肿瘤消耗的多种细胞类型和多种化学物质(氧气和/或营养物质)。与经典的两阶段肿瘤生长模型相比,多阶段模型可用于更准确地描述表现出几层组织(例如增殖组织、静止组织和坏死组织)的分层肿瘤。我们的模型由描述肿瘤演变的对流Cahn–Hilliard型方程、相关体积平均速度场的速度方程和描述化学物质密度的对流反应-扩散型方程组成。速度方程要么用达西定律表示,要么用布林克曼方程表示。我们首先构造了多相Cahn–Hilliard–Brinkman模型的全局弱解。之后,我们证明,当粘度在某种适当的意义上趋于零时,该系统的弱解收敛为多相Cahn–Hilliard–Darcy系统的弱溶液。这意味着还建立了Cahn–Hilliard–Darcy系统的全局弱解的存在性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Existence of weak solutions to multiphase Cahn–Hilliard–Darcy and Cahn–Hilliard–Brinkman models for stratified tumor growth with chemotaxis and general source terms
Abstract We investigate a multiphase Cahn–Hilliard model for tumor growth with general source terms. The multiphase approach allows us to consider multiple cell types and multiple chemical species (oxygen and/or nutrients) that are consumed by the tumor. Compared to classical two-phase tumor growth models, the multiphase model can be used to describe a stratified tumor exhibiting several layers of tissue (e.g., proliferating, quiescent and necrotic tissue) more precisely. Our model consists of a convective Cahn–Hilliard type equation to describe the tumor evolution, a velocity equation for the associated volume-averaged velocity field, and a convective reaction-diffusion type equation to describe the density of the chemical species. The velocity equation is either represented by Darcy’s law or by the Brinkman equation. We first construct a global weak solution of the multiphase Cahn–Hilliard–Brinkman model. After that, we show that such weak solutions of this system converge to a weak solution of the multiphase Cahn–Hilliard–Darcy system as the viscosities tend to zero in some suitable sense. This means that the existence of a global weak solution to the Cahn–Hilliard–Darcy system is also established.
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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