Local Existence and Stability for a Hyperbolic-elliptic System Modeling Two-phase Reservoir Flow




Schroll, Hans Joachim
Tveito, Aslak

Journal Title

Journal ISSN

Volume Title


Southwest Texas State University, Department of Mathematics


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.



Hyperbolic-elliptic system, Two-phase flow, Existence, Stability, Operator splitting, Convergence


Schroll, H. J., & Tveito, A. (2000). Local existence and stability for a hyperbolic-elliptic system modeling two-phase reservoir flow. <i>Electronic Journal of Differential Equations, 2000</i>(04), pp. 1-28.


Attribution 4.0 International

Rights Holder

This work is licensed under a Creative Commons Attribution 4.0 International License.

Rights License