The Darcy problem with porosity depending exponentially on the pressure

On the solvability of the Brinkman-Forchheimer-extended Darcy equation

The nonlinear Brinkman-Forchheimer-extended Darcy equation is used to model some porous medium flow in chemical reactors of packed bed type. The results concerning the existence and uniqueness of a weak solution are presented for nonlinear convective flows in medium with nonconstant porosity and for small data. Furthermore, the finite element approximations to the flow profiles in the fixed bed reactor are presented for several Reynolds numbers at the non-Darcy's range.

具有记忆项的Darcy定律：演化微结构的均匀化

A Darcy law with memory by homogenisation for evolving microstructure

本文通过均匀化方法，将演化微结构多孔介质中的非定常Stokes方程转化为带记忆项的Darcy型积分微分方程，并揭示了渗透系数时空依赖性与附加压力源项。

Homogenized model of immiscible incompressible two-phase flow in double porosity media : A new proof

In this paper we give a new proof of the homogenization result for an immiscible incompressible two-phase flow in double porosity media obtained earlier in the pioneer work by A. Bourgeat, S. Luckhaus, A. Mikelić (1996) and in the paper of L. M. Yeh (2006) under some restrictive assumptions. The microscopic model consists of the usual equations derived from the mass conservation laws for both fluids along with the standard Darcy-Muskat law relating the velocities to the pressure gradients and gravitational effects. The problem is written in terms of the phase formulation, i.e. where the phase …

三维Nernst-Planck-Darcy模型的长时间动力学

Long Time Dynamics Of The Three-dimensional Nernst-Planck-Darcy Model

该研究针对三维Nernst-Planck-Darcy电扩散模型，分析其全局适定性与长时间动力学，证明无外加电荷时离子浓度指数衰减至初始空间均值，存在定常电荷时存在有限维全局吸引子。

不可压缩多孔弹性介质中液体过滤的双孔隙度模型

Double Porosity Models for Liquid Filtration in Incompressible Poroelastic Media

本文基于均匀化理论，通过迭代均匀化方法推导了不可压缩多孔弹性介质中液体过滤的双孔隙度模型，得到了Biot-Terzaghi方程组及绝对刚性体的对应模型。

细薄孔隙域中斯托克斯流与对流输运的均质极限

Homogenized limits of Stokes flow and advective transport in thin perforated domains

研究细薄孔隙域中斯托克斯流与对流输运的均质化模型，推导有效方程并分析不同扩散条件下的对流-扩散行为。