Geodesic
A diffusion-convection problem with drainage arising in the ecology of mangroves
Cornelius J. van Duijn1 ; Gonzalo Galiano Casas2 ; Mark A. Peletier3
1TU Eindhoven, Netherlands
2Universidad de Oviedo, Spain
3Eindhoven University of Technology, Netherlands
Interfaces and free boundaries, Tome 3 (2001) no. 1, pp. 15-44

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DOI

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.
DOI : 10.4171/ifb/31
Classification : 46-XX, 60-XX
Mots-clés : Comparison principle, dead cores, existence, parabolic-elliptic PDEs, uniqueness

Cornelius J. van Duijn  1   ; Gonzalo Galiano Casas  2   ; Mark A. Peletier  3

1 TU Eindhoven, Netherlands
2 Universidad de Oviedo, Spain
3 Eindhoven University of Technology, Netherlands 
Cornelius J. van Duijn; Gonzalo Galiano Casas; Mark A. Peletier. A diffusion-convection problem with drainage arising in the ecology of mangroves. Interfaces and free boundaries, Tome 3 (2001) no. 1, pp. 15-44. doi: 10.4171/ifb/31
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     title = {A diffusion-convection problem with drainage arising in the ecology of mangroves},
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     pages = {15--44},
     year = {2001},
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