Existence, Uniqueness, and Continuous Dependence for a System of Hyperbolic Conservation Laws Modeling Polymer Flooding

The problem of well-posedness for a system of nonstrictly hyperbolic conservation laws is studied. A finite difference scheme is used to prove the existence of an entropy solution with bounded variation. It is proved that the entropy solution of the system is unique, and that the solution depends continuously on its initial data in a proper topology. The analysis is based on a smoothness property of one of the Riemann invariants of the system.