Advances in Differential Equations
- Adv. Differential Equations
- Volume 11, Number 8 (2006), 841-892.
On the dam problem with two fluids governed by a nonlinear Darcy's law
We consider the problem of two fluids flow through a porous medium governed by a nonlinear law. We prove the existence of a weak solution, establish the local Lipschitz continuity of this solution in the zone above the lower fluid, and prove the continuity of the upper free boundary. In the rectangular case, we prove the existence of a monotone solution with respect to the vertical variable, and the continuity of the lower free boundary. Finally, we prove the uniqueness of a monotone solution with respect to $x$ and $y$, when the dam is rectangular and the flow is governed by the linear Darcy law.
Adv. Differential Equations Volume 11, Number 8 (2006), 841-892.
First available in Project Euclid: 18 December 2012
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Challal, S.; Lyaghfouri, A. On the dam problem with two fluids governed by a nonlinear Darcy's law. Adv. Differential Equations 11 (2006), no. 8, 841--892. https://projecteuclid.org/euclid.ade/1355867618.