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A filtration problem with nonlinear Darcy’s law and generalized boundary conditions.

Carrillo Menéndez, José and Lyaghfouri, A. (2000) A filtration problem with nonlinear Darcy’s law and generalized boundary conditions. Advances in Differential Equations, 5 (4-6). pp. 515-555. ISSN 1079-9389

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Abstract

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 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.


Item Type:Article
Uncontrolled Keywords:Filtration; Dam problem; Variational inequality; Existence
Subjects:Sciences > Mathematics > Differential equations
ID Code:15953
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