MATHEMATICAL ANALYSIS FOR COMPRESSIBLE MISCIBLE DISPLACEMENT MODELS IN POROUS MEDIA
Y. AMIRAT, K. HAMDACHE, A. ZIANI
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Source: Crossref
Published: Sep 1, 1996
DOI: 10.1142/s0218202596000316
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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.
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