Electron. J. Diff. Eqns., Vol. 2000(2000), No. 04, pp. 128.
Local existence and stability for a hyperbolicelliptic system
modeling twophase reservoir flow
H. J. Schroll & A. Tveito
Abstract:
A system arising in the modeling of oilrecovery 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 apriori bounds are derived.
Applying the ArzelaAscoli theorem, local existence and uniqueness
of a classical solution for the original hyperbolicelliptic 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: Hyperbolicelliptic system, twophase flow,
existence, stability, operator splitting, convergence.
Show me the
PDF file (230K),
TEX file, and other files for this article.

Hans Joachim Schroll
Numerische Mathematik, RWTHAachen,
Templergraben 55, D52056 Aachen, Germany.
And
Mathematical Sciences,
The Norwegian University of Science and Technology,
N7491 Trondheim, Norway.
email: schroll@math.ntnu.no 

Aslak Tveito
Department of Informatics, University of Oslo,
P.O. Box 1080 Blindern, N0316 Oslo, Norway.
email: aslak@ifi.uio.no

Return to the EJDE web page