Systems of partial differential equations in porous medium

TL;DR

This paper studies a coupled system of degenerate parabolic PDEs modeling reactive solute transport in porous media, establishing existence, regularity, and finite speed of propagation of solutions, and analyzing free boundary behavior.

Contribution

It introduces a novel approach to analyze coupled PDE systems by reducing them to a scalar generalized porous medium equation, proving existence, regularity, and finite speed of solutions.

Findings

Existence of a unique weak solution for the coupled system.

Solutions propagate with finite speed, leading to free boundaries.

Interaction of initial concentrations results in complex boundary behaviors.

Abstract

We investigate systems of degenerate parabolic equations idealizing reactive solute transport in porous media. Taking advantage of the inherent structure of the system that allows to deduce a scalar Generalized Porous Medium Equation for the sum of the solute concentrations, we show existence of a unique weak solution to the coupled system and derive regularity estimates. We also prove that the system supports solutions propagating with finite speed thus giving rise to free boundaries and interaction of compactly supported initial concentrations of different species.