How Mangroves Salinize the Soil

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 diierential equations for the salt concentration and the water ow which generalizes previous models. We study the existence and uniqueness of solutions and the conditions under which the maximum principle does hold, showing a counterexample for the general situation. We also analyze 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.