On the effect of boundaries in two-phase porous flow

TL;DR

This paper investigates a mathematical model of two-fluid flow in porous media, establishing well-posedness and qualitative properties, supported by numerical simulations to understand boundary effects.

Contribution

It provides new theoretical results on the well-posedness and properties of a two-phase porous flow model, complemented by numerical analysis.

Findings

Proved local and global well-posedness of the model

Analyzed qualitative properties of the flow

Performed numerical simulations to illustrate boundary effects

Abstract

In this paper we study a model of an interface between two fluids in a porous medium. For this model we prove several local and global well-posedness results and study some of its qualitative properties. We also provide numerics.