4 papers
On the limit of a two-phase flow problem in thin porous media domains of Brinkman-type
Alaa Armiti-Juber
We study the process of two-phase flow in thin porous media domains of Brinkman-type. This is generally described by a model of coupled, mixed-type differential equations of fluids…
On the Well-posedness of a Nonlinear Fourth-Order Extension of Richards' Equation
Alaa Armiti-Juber, Christian Rohde
We study a nonlinear fourth-order extension of Richards' equation that describes infiltration processes in unsaturated soils. We prove the well-posedness of the fourth-order equati…
Existence of weak solutions for a nonlocal pseudo-parabolic model for Brinkman two-phase flow in asymptotically flat porous media
Alaa Armiti-Juber, Christian Rohde
We study a nonlocal evolution equation that involves a pseudo-parabolic third-order term. The equation models almost uni-directional two-phase flow in Brinkman regimes. We prove th…
On Darcy-and Brinkman-Type Models for Two-Phase Flow in Asymptotically Flat Domains
Alaa Armiti-Juber, Christian Rohde
We study two-phase flow for Darcy and Brinkman regimes. To reduce the computational complexity for flow in vertical equilibrium various simplified models have been suggested. Examp…