A variational principle for problems of steady-state ground water flow with a free surface

Abstract

The problem of steady-state free surface ground water flow through a porous medium is represented in the form of a variational principle for a functional dependent on the flow domain. It is proved that on the region to be found this functional takes a minimum value. This variational principle is generalized to include the flow models that allow the presence of partially saturated zones in the medium. On simple examples it is shown how the variational formulation can be used for proving the existence or absence of solutions.