Gagneux, Gérard Une étude théorique sur la modélisation de G. Chavent des techniques d’exploitation secondaire des gisements pétrolifères. (French) Zbl 0545.76116 J. Méc. Théor. Appl. 2, 33-56 (1983). Summary: The aim of this paper is the theoretical study of water-oil displacements in a 2-D or 3-D porous field, with reference to G. Chavent’s modelization [e.g.: Lect. Notes Math. 503, 258-270 (1976; Zbl 0346.76071)]. This mathematical model, which takes into account the ”well- effect” on the outflow boundary, involves a degenerated nonlinear diffusion-convection equation. The degenerate case of immiscible displacements is approached through a non-degenerate problem for which the existence of a unique strong solution is proved. The study of the said problem is shown to prove the existence of a solution for the degenerated problem and some of its properties: decrease, asymptotic behaviour, dependence on the initial data, uniqueness in some particular cases. Cited in 2 Documents MSC: 76T99 Multiphase and multicomponent flows 76S05 Flows in porous media; filtration; seepage Keywords:water-oil displacements; 2-D or 3-D; G. Chavent’s modelization; well-effect; outflow boundary; degenerated nonlinear diffusion-convection equation; immiscible displacements; unique strong solution; decrease, asymptotic behaviour, dependence on the initial data, uniqueness Citations:Zbl 0346.76071 PDFBibTeX XMLCite \textit{G. Gagneux}, J. Méc. Théor. Appl. 2, 33--56 (1983; Zbl 0545.76116)