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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

Official URL: http://www.aftabi.com/advancesindiffer.html

URL | URL Type |
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http://www.aftabi.com | Publisher |

## 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 |
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Uncontrolled Keywords: | Filtration; Dam problem; Variational inequality; Existence |

Subjects: | Sciences > Mathematics > Differential equations |

ID Code: | 15953 |

Deposited On: | 13 Jul 2012 10:55 |

Last Modified: | 12 Dec 2018 15:07 |

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