Systems of partial differential equations in porous medium. (March 2016)

• Record Type: Journal Article
• Authors: Kuusi, Tuomo; Monsaingeon, Léonard; Videman, Juha
• Is Part Of: Nonlinear analysis. Volume 133(2016)
• Page Start: 79
• Page End: 101
• Publication Date: 2016-03
• Subjects: Porous medium equation -- Freundlich and Langmuir isotherms -- Existence -- Uniqueness -- Regularity; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.11.015
• Languages: English
• ISSNs: 0362-546X

Abstract

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.