A refined and extended mathematical model for the non-equilibrium two-phase (water-oil) flows in porous media is presented. We give here the basic problem statements and more special equations and show the results of a rigorous investigation of an important class of intermediate asymptotic solutions, the travelling waves.We discuss here also peculiar properties of the solutions to the capillary-imbibition problem which demonstrate clearly arising new effects.
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Баренблатт et al. (1997) studied this question.
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