Existence of weak solutions for a nonlocal pseudo-parabolic model for Brinkman two-phase flow in asymptotically flat porous media

TL;DR

This paper proves the existence of weak solutions for a nonlocal pseudo-parabolic model describing two-phase flow in porous media and demonstrates its behavior through numerical examples.

Contribution

It establishes the existence of weak solutions for a novel nonlocal pseudo-parabolic equation modeling two-phase flow in porous media.

Findings

The model supports overshooting phenomena.

Numerical simulations explore solution behavior in different regimes.

The equation accurately captures flow dynamics in asymptotically flat media.

Abstract

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 the existence of weak solutions for this equation. We also give a series of numerical examples that demonstrate the ability of the equation to support overshooting and explore the behavior of solutions in various limit regimes.