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Séminaire de EDP - Physique Mathématique

The Muskat problem in unstable regimes

Angel Castro

( Madrid )

Salle 2

le 05 mars 2019 à 11:30

In this talk we will consider the Incompressible Porous Media equation with an initial data of Muskat type in the unstable regime. After discussing the physics of the problem, we will show how the convex integration allows us to construct solutions of mixing type in this situation in which the classical Muskat equation is ill-posed. Also, we will present some new results addressing the construction of solutions in the partial unstable regime.