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.