Stability of a Resonant System of Conservation Laws Modeling Polymer Flow with Gravitation

We prove L1 uniqueness and stability for a resonant 2×2 system of conservation laws that arise as a model for two phase polymer flow in porous media. The analysis uses the equivalence of the Eulerian and Lagrangian formulation of this system, and the results are first established for an auxiliary scalar equation. Our methods are based on front tracking approximations for the auxiliary equation, and the Kru kov entropy condition for scalar conservation laws.