L1{contraction and Uniqueness for Unstationary Saturated{unsaturated Porous Media Flow

We prove L 1 {contraction and thus uniqueness for solutions of the equation modelling un-stationary saturated{unsaturated water ow in porous media. Due to three diierent types of boundary conditions, describing contact with an impervious layer, with water reservoirs of variable level and with the atmosphere, this elliptic{parabolic equation comes as a varia-tional inequality with time{dependent constraints at the boundary. The notion of solution considered is the weakest possible: solutions of nite energy. In particular, we do not assume any time{regularity of the saturation s like @ t s 2 L 1 (Q) : The proof applies a technique developed by the author for general elliptic{parabolic equations .