Geodesic
Global weak solutions for a degenerate parabolic system modelling a one-dimensional compressible miscible flow in porous media
Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 1, pp. 109-128

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We show the solvability of a nonlinear degenerate parabolic system of two equations describing the displacement of one compressible fluid by another, completely miscible with the first, in a one-dimensional porous medium, neglecting the molecular diffusion. We use the technique of renormalised solutions for parabolic equations in the derivation of a priori estimates for viscosity type solutions. We pass to the limit, as the molecular diffusion coefficient tends to 0, on the parabolic system, owing to compensated compactness arguments. 
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     author = {Amirat, Y. and Ziani, A.},
     title = {Global weak solutions for a degenerate parabolic system modelling a one-dimensional compressible miscible flow in porous media},
     journal = {Bollettino della Unione matematica italiana},
     pages = {109--128},
     publisher = {mathdoc},
     volume = {Ser. 8, 7B},
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     year = {2004},
     zbl = {1117.35038},
     mrnumber = {MR2044263},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_1_a4/}
}
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Amirat, Y.; Ziani, A. Global weak solutions for a degenerate parabolic system modelling a one-dimensional compressible miscible flow in porous media. Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 1, pp. 109-128. http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_1_a4/