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

作　　者：肖翔宇 蒲志林 

机构地区：[1]四川师范大学数学科学学院,四川 成都

出　　处：《应用数学进展》2021年第7期2428-2441,共14页Advances in Applied Mathematics

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。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.

关 键 词：耦合 存在性 唯一性 能量估计 

分 类 号：O17[理学—数学]