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Electronic Journal of Differential Equations
A system arising in the modeling of oil-recovery processes is analyzed. It consists of a hyperbolic conservation law governing the saturation and an elliptic equation for the pressure. By an operator splitting approach, an approximate solution is constructed. For this approximation appropriate a-priori bounds are derived. Applying the Arzela-Ascoli theorem, local existence and uniqueness of a classical solution for the original hyperbolic-elliptic system is proved. Furthermore, convergence offatcat:4t6ffqa6kjbq5aoeelc5ftyxse