Geodesic
Self-similar solutions of the equations of two-component isothermal transport in porous media with phase transitions
Matematičeskoe modelirovanie, Tome 18 (2006) no. 7, pp. 53-60

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In the present paper it is considered a two-component multiphase isothermal flow of compressible fluids in porous media with mass exchange between phases. The system of equations has discontinuous solutions with concentration waves. For the equations the auto modeling decisions “traveling wave” are found. Such decisions describe running waves of concentration at continuous pressure. The cases, when on the one hand of concentration jump the solution is in single-phase state, and with another is in a two-phase state, are considered. 
@article{MM_2006_18_7_a3,
     author = {E. V. Koldoba},
     title = {Self-similar solutions of the equations of two-component isothermal transport in porous media with phase transitions},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {53--60},
     publisher = {mathdoc},
     volume = {18},
     number = {7},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2006_18_7_a3/}
}
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E. V. Koldoba. Self-similar solutions of the equations of two-component isothermal transport in porous media with phase transitions. Matematičeskoe modelirovanie, Tome 18 (2006) no. 7, pp. 53-60. http://geodesic.mathdoc.fr/item/MM_2006_18_7_a3/