Stability of a resonant system of conservation laws modeling polymer flow with gravitation

We prove L-1 uniqueness and stability for a resonant 2 x 2 system of conser vation laws that arise as a model for two phase polymer flow in porous medi a. The analysis uses the equivalence of the Eulerian and Lagrangian formula tion of this system. and the results are first established for an auxiliary scalar equation. Our methods are based oil front tracking approximations f or the auxiliary equation and the Kruzkov entropy condition for scalar cons ervation laws. (C) 2001 Academic Press.