A minmax formulation of nonlinear seepage flow problem

Abstract

Starting from the potential character of the non-linear flow model of fluid through rigid isotropic porous media, a general strategy to build up a minmax variational formulation is presented. A consistent extension of the theoretical framework to anisotropic porous media is straightforwardly obtained. A geometrical interpretation to the reciprocal functional in terms of suitable norms of kinematic field is given. A physical interpretation of Legendre-Fenkel transform strictly related to the dissipation of mechanical power is emphasized. The abstract results are finally applied to quadratic and cubic flow models and the strict convexity of the related functionals is proved, with relevant implications on computational aspects.