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Angel Castro; Diego Córdoba; Francisco Gancedo
Some recent results on the Muskat problem
Journées équations aux dérivées partielles (2010), Exp. No. 5, 14 p., doi: 10.5802/jedp.62
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Résumé - Abstract

We consider the dynamics of an interface given by two incompressible fluids with different characteristics evolving by Darcy’s law. This scenario is known as the Muskat problem, being in 2D mathematically analogous to the two-phase Hele-Shaw cell. The purpose of this paper is to outline recent results on local existence, weak solutions, maximum principles and global existence.

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