The dam problem for linear Darcy’s law and nonlinear leaky boundary conditions. (English) Zbl 0947.35177

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.


35R35 Free boundary problems for PDEs
35Q35 PDEs in connection with fluid mechanics
76D27 Other free boundary flows; Hele-Shaw flows