Systems of partial differential equations in porous medium
Analysis of PDEs
2014-12-19 v2
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.
Keywords
Cite
@article{arxiv.1412.5414,
title = {Systems of partial differential equations in porous medium},
author = {Tuomo Kuusi and Léonard Monsaingeon and Juha Videman},
journal= {arXiv preprint arXiv:1412.5414},
year = {2014}
}