动力学边界条件或移动接触线的多孔介质中二相流模型具有广泛的应用背景和重要的研究价值。在对多孔介质中二相流扩散界面模型理论研究中亟待解决的数学难点问题进行系统梳理的基础上，本项目拟应用非线性泛函分析、偏微分方程与无穷维动力系统理论分别对具有这两种边界条件的三维Cahn-Hilliard-Brinkman系统进行研究，深入探讨具有动力学边界条件的此系统吸引子的问题，并解析此系统移动接触线问题解的存在性、唯一性及长时间动力学行为。本项目是实际应用驱动的数学理论和方法的研究，不仅为该问题数值格式的设计和算法的实现提供相应的理论依据，还对探索Brinkman多孔介质中二相流相分离的基本规律和物理机制具有重要的理论指导意义。

The two-phase flow models in porous media with dynamic boundary conditions or moving contact lines are widely applied in various of fields and of great value in research. Based on the systematic analysis of mathematical difficulties for the diffuse-interface models of two-phase flow in porous media , the objective of this project is to study the three-dimensional Cahn-Hilliard-Brinkman systems with the two different kinds of boundary conditions,respectively, by virtue of the theories of nonlinear functional analysis, partial differential equations and infinite dimensional dynamical systems. We deeply discuss the dynamics of such system with dynamic boundary conditions and consider the well-posedness as well as the long-time behavior of solutions for such system with moving contact lines. This project focuses on the studies of the mathematical theory and methods in practical applications, which not only plays an important role in designing more appropriate numerical schemes and understanding numerical simulations, but also reveals the basic law and physical mechanism of phase decomposition of the binary fluid flow in a Brinkman porous medium.