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

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dc.contributor.authorSchroll, Hans Joachim
dc.contributor.authorTveito, Aslak
dc.date.accessioned2020-01-07T15:58:44Z
dc.date.available2020-01-07T15:58:44Z
dc.date.issued2000-01-05
dc.description.abstractA 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.
dc.description.departmentMathematics
dc.formatText
dc.format.extent28 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationSchroll, 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.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/9140
dc.language.isoen
dc.publisherSouthwest Texas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.holderThis work is licensed under a Creative Commons Attribution 4.0 International License.
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2000, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectHyperbolic-elliptic system
dc.subjectTwo-phase flow
dc.subjectExistence
dc.subjectStability
dc.subjectOperator splitting
dc.subjectConvergence
dc.titleLocal Existence and Stability for a Hyperbolic-elliptic System Modeling Two-phase Reservoir Flow
dc.typeArticle

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