Integrable seepage equations

Well-known results of the classification of parabolic-type differential equations, possessing an infinite Lie-Bäcklund algebra, are used to describe seepage models, which, using (in general) differential substitutions, can be reduced to the heat conduction equation. Relations between the functional parameters, characterizing the properties of the liquid and gas phases and the porous medium, are obtained that ensure the existence of such substitutions.