Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 04, pp. 1-28.

Title: Local existence and stability for a  hyperbolic-elliptic system 
        modeling two-phase reservoir flow 

Authors: H. J. Schroll (RWTH-Aachen, Germany)
         A. Tveito (University of Oslo, Norway)

Abstract: 
 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 of the approximation generated by 
 operator splitting towards the unique solution follows.
 It is also proved that  the unique solution is stable with respect to
 perturbations of the initial data.

Submitted March 10, 1999. Published January 5, 2000.
Math Subject Classifications: 35M10, 35L45, 35J25.
Key Words: Hyperbolic-elliptic system; two-phase flow; 
           existence; stability; operator splitting; convergence.