Local existence and stability for a hyperbolic-elliptic system modeling two-phase reservoir flow
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1224295
- author
- Schroll, Achim LU and Tveito, Aslak
- organization
- publishing date
- 2000
- 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
- 2016-04-04 08:55:38
- date last changed
- 2018-11-21 20:50:15
@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}}, url = {{http://ejde.math.txstate.edu/}}, volume = {{2000}}, year = {{2000}}, }