| Abstract: | For the stationary problem of the nonlinear filtration in a bounded domain, from variational principles one establishes a series of statements: for a fixed drop in pressure, an increase in the local filtration resistance or a symmetrization of the domain leads to a decrease of the modified flow rate; at a depression inside the domain of the entrance-surface, the flow and the velocity of the filtration do not decrease at any point of the outgoing surface, etc. When passing to an unbounded domain, it turnsout that at a filtration with a limit gradient, there may exist physically distinct solutions, which are confirmed by examples given In the paper. |
