The dam problem for linear Darcy's law and nonlinear leaky boundary conditions (Q1977664)

This work is devoted to the study of a model for a dam problem with a general geometry and a general permeability matrix. Instead of the classical Dirichlet boundary conditions the authors assumed that the flux of the fluid is governed by a function of the difference between the pressure inside and outside the porous medium. Such conditions are called ``leaky boundary conditions''. The authors established properties of solutions and the regularity of the free boundary and proved a comparison result from which they deduced some uniqueness results.