Carrillo Menéndez, JoséLyaghfouri, A.2023-06-202023-06-2020001079-9389https://hdl.handle.net/20.500.14352/57446This article studies a filtration problems with nonlinear Darcy’s law, e.g. ~v = −|rp|q−2rp, where p is the fluid pressure , q > 1, and ~v is the velocity, governed by the mass conservation law div(~v) = 0. This leads to a free boundary problem since the movement of the fluid takes place only in the “wet part” of the domain which is also unknown. The authors give a unified formulation of the problem to include general boundary conditions, such as Dirichlet, Neumann, and so-called leaky boundary conditions. The existence of (weak) solutions is established, for both bounded and unbounded domains, by an approximation method.journal articlehttp://www.aftabi.com/advancesindiffer.htmlhttp://www.aftabi.commetadata only access517.9FiltrationDam problemVariational inequalityExistenceEcuaciones diferenciales1202.07 Ecuaciones en Diferencias