Global weak solutions for a degenerate parabolic system modelling a one-dimensional compressible miscible flow in porous media
Amirat, Y. ; Ziani, A.
Bollettino dell'Unione Matematica Italiana, Tome 7-A (2004), p. 109-128 / Harvested from Biblioteca Digitale Italiana di Matematica
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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.

Proviamo la risolubilità di un sistema parabolico non lineare degenere costituito da due equazioni che descrivono lo spostamento di un fluido compressibile, causato da un altro fluido, completamente miscibile al primo, in un mezzo poroso unidimensionale, trascurando la diffusione molecolare. Usiamo la tecnica delle soluzioni rinormalizzate per le equazioni paraboliche al fine di ottenere stime a priori per soluzioni di tipo viscosità. Passiamo al limite nel sistema parabolico, quando il coefficiente di diffusione molecolare tende a zero, tramite metodi di compattezza per compensazione.

Publié le : 2004-02-01
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     author = {Y. Amirat and A. Ziani},
     title = {Global weak solutions for a degenerate parabolic system modelling a one-dimensional compressible miscible flow in porous media},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {7-A},
     year = {2004},
     pages = {109-128},
     zbl = {1117.35038},
     mrnumber = {2044263},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2004_8_7B_1_109_0}
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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 dell'Unione Matematica Italiana, Tome 7-A (2004) pp. 109-128. http://gdmltest.u-ga.fr/item/BUMI_2004_8_7B_1_109_0/

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