Global weak solutions of a three-dimensional flow model for a multi-species mixture in porous media

We consider an initial boundary value problem for a non-linear differential system consisting of one equation of parabolic type coupled with a n × n semi-linear hyperbolic system of first order. This system of equations describes the compressible miscible displacement of n + 1 chemical species in a porous medium, in the absence of diffusion and dispersion. We assume the viscosity of the fluid mixture to be constant. We prove, in three space dimensions, the existence of a global weak solution with non-smooth initial data for the concentration. The proof is based on the artificial viscosity method together with a compensated compactness argument. © 1998 B. G. Teubner Stuttgart—John Wiley & Sons, Ltd.