A degenerate elliptic-parabolic system arising in competitive contaminant transport

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.