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Abstract
We consider a model describing two-phase immiscible and incompressible flows in a porous medium made of different rock types. This model leads to two coupled non-linear equations, the first one is elliptic and the other one is a degenerated equation of advection-diffusion, with nonlinear transmission conditions at the interface between different rock types. By mean of a mixed formulation, we obtain a result of existence and we give some results on the uniqueness.