Mathematical analysis for compressible miscible displacement models in porous media. (English) Zbl 0859.35087

Amirat, Y.; Hamdache, K.; Ziani, A.

Math. Models Methods Appl. Sci. 6, No. 6, 729-747 (1996).

Authors’ summary: “We discuss a three-dimensional displacement model of one miscible compressible fluid by another in a porous medium. The motion is modeled by a nonlinear system of parabolic type coupling the pressure and the concentration. We give an existence result of weak solutions for a model with diffusion and dispersion, using the Schauder fixed point theorem. We also study a model in the absence of diffusion and dispersion. The system becomes of parabolic-hyperbolic type, the existence of global weak solutions is then obtained through a compensated compactness argument”.

Reviewer: M.Biroli (Monza)

MSC:

35Q30	Navier-Stokes equations
35D05	Existence of generalized solutions of PDE (MSC2000)
76S05	Flows in porous media; filtration; seepage

Keywords:

model without diffusion and dispersion; three-dimensional displacement model; compressible fluid; porous medium; model with diffusion and dispersion; Schauder fixed point theorem; compensated compactness