Analysis Seminar - 6/5/2015

Wednesday, 6 May 2015, 1:00 p.m.

Lecturer: Juha H. Videman, CAMGSD & DM, IST-UL

Title: "On systems of PDEs modeling competitive contaminant transport in porous media"

Local: Room 1.6, Edifício VII

Faculdade de Ciências e Tecnologia, Quinta da Torre, Caparica

Abstract: The transport of contaminants in subsurface environments is a complex process modeled by advection-diff usion-reaction equations. If the reactive adsorption process (accumulation of a pollutant on the porous matrix) is described by a nonlinear isotherm of Freundlich type, the evolution of the solute concentrations is governed by a degenerate parabolic equation. In the multi-species case (contamination by several solutes), this corresponds to a coupled system of Generalized Porous Medium Equations (GPME). 

After introducing the basic concepts of modeling contaminant transport in porous media, I will discuss our recent results on a GMPE system arising from, but not limited to, competitive contaminant transport. Taking advantage of the inherent structure of the system that allows to deduce a scalar GPME for the sum of the solute concentrations, we show existence of a unique weak solution and prove that the system supports solutions propagating with fi nite speed thus giving rise to free boundaries and interaction of compactly supported initial concentrations of diff erent species.

This is a joint work with Tuomo Kuusi (Aalto University) and Léonard Monsaingeon (IST).