Hele-Shaw流模型的Darcy-Cahn-Hilliard方程组解的研究
Study on Darcy-Cahn-Hilliard Equations of Hele-ShawFlow
DOI: 10.12677/AAM.2021.107255, PDF, HTML, 下载: 299  浏览: 3,559 
作者: 肖翔宇, 蒲志林:四川师范大学数学科学学院,四川 成都
关键词: 耦合存在性唯一性能量估计Coupled Existence Uniqueness Energy Estimate
摘要: 本文对由Darcy方程和Cahn-Hilliard方程耦合而成的两相Hele-Shaw流扩散界面模型进行了研究。在此模型中,Darcy方程中的额外相位诱导力项和Cahn-Hilliard方程中的流体诱导输运项耦合了两相方程,本文对方程组中的非线性项在满足更一般假设条件下,研究了方程组弱解的存在性和唯一性及解的能量估计。
Abstract: In this paper, we study the two phase Hele-Shaw flow, which consists of the Cahn Hilliard eqution and the Darcy equation. In this model, an extra phase induced force term in the Darcy equation is coupled with a fluid induced transport term in the Cahn-Hilliard equation. As the non-linear term satisfies the more general condition, we show the existence of the weak solution, energy estimate, and the uniqueness.
文章引用:肖翔宇, 蒲志林. Hele-Shaw流模型的Darcy-Cahn-Hilliard方程组解的研究[J]. 应用数学进展, 2021, 10(7): 2428-2441. https://doi.org/10.12677/AAM.2021.107255

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