Filtration of a piecewise-homogeneous liquid

The nonsteady filtration of two immiscible liquids, in the absence of pressure, in a homogeneous and isotropic porous medium, is considered. A nonlinear hydrodynamic problem is formulated, and a number of its features are noted. The solution of the corresponding linearized problem is obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 62–69, November–December, 1976.