  We study the Cauchy problem of a $3\times 3$ system of conservation laws
modeling two--phase flow of polymer flooding in rough porous media with
possibly discontinuous permeability function. The system loses strict
hyperbolicity in some regions of the domain where the eigenvalues of different
families coincide, and BV estimates are not available in general. For a
suitable $2\times 2$ system, a singular change of variable introduced by Temple
could be effective to control the total variation. An extension of this
technique can be applied to a $3\times 3$ system only under strict hypotheses
on the flux functions. In this paper, through an adapted front tracking
algorithm we prove the existence of solutions for the Cauchy problem under mild
assumptions on the flux function, using a compensated compactness argument.

Analysis of PDEs