We consider both stationary and time-dependent versions of a model describing the vertical movement of water and salt in a porous medium in which a continuous extraction of water takes place (by the roots of mangroves). The problem is formulated in terms of a coupled system of partial differential equations for the salt concentration and the water flow which generalizes previous models. We study the existence and uniqueness of solutions and the conditions under which the maximum principle does hold, showing a counter-example for the general situation. We also analyse the stability of the steady state solution. Finally, we investigate the occurrence of dead cores (sets where the threshold salt concentration is attained) by means of the comparison principle in the stationary problem and of suitable energy estimates in the evolution problem.
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Cornelius J. van Duijn, Gonzalo Galiano Casas, Mark A. Peletier, A diffusion-convection problem with drainage arising in the ecology of mangroves. Interfaces Free Bound. 3 (2001), no. 1, pp. 15–44DOI 10.4171/IFB/31