Advances in Differential Equations

The dam problem for linear Darcy's law and nonlinear leaky boundary conditions

M. Chipot and A. Lyaghfouri

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Starting from the model proposed in [15], we study a stationary flow of fluid, governed by a linear Darcy's law, through an inhomogeneous porous medium with leaky boundary conditions. We establish properties of solutions and regularity of the free boundary. Finally, we prove a comparison result from which we deduce some uniqueness results.

Article information

Adv. Differential Equations, Volume 3, Number 1 (1998), 1-50.

First available in Project Euclid: 19 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35R35: Free boundary problems
Secondary: 35Q35: PDEs in connection with fluid mechanics 76S05: Flows in porous media; filtration; seepage


Chipot, M.; Lyaghfouri, A. The dam problem for linear Darcy's law and nonlinear leaky boundary conditions. Adv. Differential Equations 3 (1998), no. 1, 1--50.

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