%0 Journal Article
%A Carrillo Menéndez, José
%A Lyaghfouri, A.
%T A filtration problem with nonlinear Darcy’s law and generalized boundary conditions.
%D 2000
%@ 1079-9389
%U https://hdl.handle.net/20.500.14352/57446
%X This 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 conservationlaw 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 anapproximation method.
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