Analyse mathématique de modèles non linéaires de l'ingénierie pétrolière / Gérard Gagneux, Monique Madaune-Tort

Auteur: Gagneux, Gérard - AuteurCo-auteur: Madaune-Tort, Monique (1951-) - AuteurAuteur secondaire : Marle, Charles-Michel (1934-) - PréfacierType de document: MonographieCollection: Mathématiques et applications ; 22Langue: françaisPays: AllemagneÉditeur: Berlin : Springer, 1996Description: 1 vol. (XVI-187 p.) : ill. ; 24 cm ISBN: 3540605886 ; br. Résumé: This book is devoted to the mathematical analysis of nonlinear multi-fluid models in the oil industry. It contains a systematic description of the mathematical modeling in this domain. For isothermal dead oil, the authors use a model described by an initial-boundary value problem for a diffusion-convection equation coupled with an elliptic equation. In general, the diffusion-convection equation may be degenerate. The existence of weak solutions is shown by a fixed-point method. In some particular cases, the uniqueness and regularity of solutions are obtained. The hyperbolic phenomena in the degenerate case are also discussed. Finally, the limit as the diffusion term tends to zero is studied, which leads to the existence and uniqueness of entropy solutions for the scalar conservation law with boundary condition. The presentation of this book is clear and self-contained. This makes it accessible for graduate students and researchers in the area of partial differential equations. (MathSciNet).Bibliographie: Bibliogr. p. [171]-183. Index. Sujets MSC: 35Q62 Partial differential equations -- Equations of mathematical physics and other areas of application -- PDEs in connection with statistics
35Q68 Partial differential equations -- Equations of mathematical physics and other areas of application -- PDEs in connection with computer science
35F25 Partial differential equations -- General first-order equations and systems -- Initial value problems for nonlinear first-order equations
76S05 Fluid mechanics -- Flows in porous media; filtration; seepage -- Flows in porous media; filtration; seepage
76Txx Fluid mechanics -- Two-phase and multiphase flows
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Bibliogr. p. [171]-183. Index

This book is devoted to the mathematical analysis of nonlinear multi-fluid models in the oil industry. It contains a systematic description of the mathematical modeling in this domain. For isothermal dead oil, the authors use a model described by an initial-boundary value problem for a diffusion-convection equation coupled with an elliptic equation. In general, the diffusion-convection equation may be degenerate. The existence of weak solutions is shown by a fixed-point method. In some particular cases, the uniqueness and regularity of solutions are obtained. The hyperbolic phenomena in the degenerate case are also discussed. Finally, the limit as the diffusion term tends to zero is studied, which leads to the existence and uniqueness of entropy solutions for the scalar conservation law with boundary condition. The presentation of this book is clear and self-contained. This makes it accessible for graduate students and researchers in the area of partial differential equations. (MathSciNet)

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