Global weak solutions to equations of compressible miscible flows in porous media

We study the one-dimensional equations governing compressible flows of m miscible components in a porous medium. The equations are reduced to a quasi-linear parabolic system for the discharge function P and the concentrations c(i). The equations of this system are strongly coupled since the parabolic equation for c(i) contains both the second derivative c(ixx) and the second derivative P-xx. We prove global weak solvability of an initial boundary- value problem both in the Eulerian and Lagrangian formulations.