A degenerate elliptic-parabolic system arising in competitive contaminant transport

TL;DR

This paper studies a complex degenerate elliptic-parabolic PDE system modeling reactive solute transport in groundwater, proving existence, uniqueness, non-negativity, and exploring finite speed of propagation through numerical simulations.

Contribution

It establishes the existence and uniqueness of weak solutions for a coupled nonlinear PDE system with physically reasonable conditions, and investigates propagation properties numerically.

Findings

Unique weak solution exists under certain conditions.

Solute concentrations remain non-negative with non-negative sources.

Numerical results show finite speed of propagation of solutes.

Abstract

In this work we investigate a coupled system of degenerate and nonlinear partial differential equations governing the transport of reactive solutes in groundwater. We show that the system admits a unique weak solution provided the nonlinear adsorption isotherm associated with the reaction process satisfies certain physically reasonable structural conditions. We conclude, moreover, that the solute concentrations stay non-negative if the source term is componentwise non-negative and investigate numerically the finite speed of propagation of compactly supported initial concentrations, in a two-component test case.