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

Schroll, Achim LU and Tveito, Aslak (2000) In Electronic Journal of Differential Equations 2000(4). p.1-28
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.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Electronic Journal of Differential Equations
volume
2000
issue
4
pages
1 - 28
publisher
Texas State University - San Marcos Department of Mathematics
ISSN
1550-6150
language
English
LU publication?
yes
id
50f9870c-be85-4a24-9553-4eb33006d576 (old id 1224295)
alternative location
http://ejde.math.txstate.edu/
date added to LUP
2008-09-02 12:13:33
date last changed
2016-04-16 06:06:07
@article{50f9870c-be85-4a24-9553-4eb33006d576,
  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.},
  author       = {Schroll, Achim and Tveito, Aslak},
  issn         = {1550-6150},
  language     = {eng},
  number       = {4},
  pages        = {1--28},
  publisher    = {Texas State University - San Marcos Department of Mathematics},
  series       = {Electronic Journal of Differential Equations},
  title        = {Local existence and stability for a hyperbolic-elliptic system modeling two-phase reservoir flow},
  volume       = {2000},
  year         = {2000},
}