Analyse mathématique de modèles non linéaires de l'ingénierie pétrolière / Gérard Gagneux, Monique Madaune-Tort ; préf. de Charles-Michel Marle

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)