In this paper, we study degenerate parabolic system, which is strongly coupled. We prove general existence result, but the uniqueness remains an open question. Our proof of existence is based on a crucial entropy estimate which both control the gradient of the solution and the non-negativity of the solution. Our system are of porous medium type and our method applies to models in seawater intrusion.

In this paper, we consider the Föppl-von Kàrmàn equations in the case of a simply supported thin plate. We introduce a nonlinear Gauss-Seidel fixed point scheme which allows to obtain a constructive proof of the existence and the uniqueness, when a small nonzero source term is considered. Numerical simulations are given using finite elements approximation. We point out the important role of a parameter which allows to select situations in which a buckling phenomena is observed numerically. KEYWORDS buckling phenomena, finite elements approximation, Föppl-von Kàrmàn equations, unique weak solution MSC CLASSIFICATION 35G60; 65N30

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